GaN single crystal substrate having a large area and a main surface whose plane orientation is other than (0001) and (000-1)

ABSTRACT

A GaN single crystal substrate has a main surface with an area of not less than 10 cm 2 , the main surface has a plane orientation inclined by not less than 65° and not more than 85° with respect to one of a (0001) plane and a (000-1) plane, and the substrate has at least one of a substantially uniform distribution of a carrier concentration in the main surface, a substantially uniform distribution of a dislocation density in the main surface, and a photoelasticity distortion value of not more than 5×10 −5 , the photoelasticity distortion value being measured by photoelasticity at an arbitrary point in the main surface when light is applied perpendicularly to the main surface at an ambient temperature of 25° C. Thus, the GaN single crystal substrate suitable for manufacture of a GaN-based semiconductor device having a small variation of characteristics can be obtained.

This application is a continuation of U.S. application Ser. No.12/817,753, filed Jun. 17, 2010, the entire contents of which isincorporated herein by reference. U.S. application Ser. No. 12/817,753claims the benefit of Japanese Patent Application No. 2009-204977, filedon Sep. 4, 2009, Japanese Patent Application No. 2009-204978, filed onSep. 4, 2009 and Japanese Patent Application No. 2009-227496, filed onSep. 30, 2009.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a GaN single crystal substrate suitablefor manufacture of a GaN-based semiconductor device havingcharacteristics with small variations, specifically to a GaN singlecrystal substrate having a large area and a main surface whose planeorientation is other than (0001) and (000-1) (namely other than {0001}),and having at least one of a substantially uniform distribution of thecarrier concentration in the main surface, a substantially uniformdistribution of the dislocation density in the main surface, and a smallphotoelasticity distortion in the main surface that is a distortionmeasured by photoelasticity, and relates to a method of manufacturingthe GaN single crystal substrate. The invention also relates to aGaN-based semiconductor device including such a GaN single crystalsubstrate and at least one GaN-based semiconductor layer formed on themain surface of the substrate, and a method of manufacturing theGaN-based semiconductor device.

2. Description of the Background Art

Group III nitride crystals used suitably for light emitting devices,electronic devices, semiconductor sensors and the like are usuallymanufactured by means of vapor phase methods such as HVPE (hydride vaporphase epitaxy) and MOCVD (metal organic chemical vapor deposition), andliquid phase methods such as flux method, to grow a crystal on a mainsurface of a sapphire substrate where the main surface is a (0001)plane, or a main surface of a GaAs substrate where the main surface is a(111) A plane. Therefore, a group III nitride crystal as usuallyobtained has a main surface whose plane orientation is {0001}

Regarding a light emitting device including a substrate of a group IIInitride crystal having a main surface whose plane orientation is {0001},and a light emitting layer of an MQW (multiple quantum well) structureon the main surface, the polarity in the <0001> direction of the groupIII nitride crystal causes spontaneous polarization in the lightemitting layer, resulting in a large blue shift of light emission and adeteriorated luminous efficacy. A group III nitride crystal having amain surface whose plane orientation is other than {0001} is thereforeneeded.

In order to meet such a need, Japanese Patent Laying-Open No.2008-143772 (Patent Document 1) discloses a method of manufacturing agroup III nitride crystal having a main surface whose plane orientationhas an off angle of 5° or less with respect to one of the planeorientations {1-10X}(where X is an integer of not less than 0),{11-2Y}(where Y is an integer of not less than 0), and {HK−(H+K)0}(where H and K are each an integer other than 0), specifically a mainsurface whose plane orientation is one of {1-100}, {11-20}, {1-102},{11-22}, {12-30}, and {23-50}.

Even if the manufacturing method disclosed in Japanese PatentLaying-Open No. 2008-143772 (Patent Document 1) is used, the group IIInitride crystal grown on the main surface whose plane orientation is{1-100}, {11-20} or {23-50} is partially polycrystallized, resulting ina problem that a single crystal substrate of a large area is difficultto obtain. Further, at a crystal growth surface of the group III nitridecrystal grown on the main surface having the plane orientation {1-102}or {11-22}, a facet with the plane orientation {0001} and a facet with aplane orientation other than {0001} are generated.

Here, the efficiency in taking in impurities from a facet of the planeorientation {0001} is considerably different from that from a facet of aplane orientation other than {0001}. A resultant problem is therefore alarge variation of the carrier concentration and a large variation ofthe specific resistance in the main surface of the group III nitridecrystal having been grown, and accordingly large variations ofcharacteristics of a semiconductor device for which such a substrate isused.

Further, in a growth portion where a facet of the plane orientation of{0001} is a crystal growth surface, dislocation propagatesperpendicularly to the {0001} plane (namely the <0001> direction). In agrowth portion where a facet of a plane orientation other than {0001} isa crystal growth surface, dislocation propagates in parallel with the{0001} plane. A resultant problem is therefore a large variation of thedislocation density in the main surface of a grown group III nitridecrystal, and thus large variations of characteristics of a semiconductordevice using such a substrate.

Furthermore, because of a large variation of the dislocation density inthe main surface of the grown group III nitride crystal, a group IIInitride crystal substrate made from such a group III nitride crystal hasa main surface in which a microscopic variation of distortion isgenerated, resulting in a problem that a large local distortion isgenerated.

Japanese Patent Laying-Open No. 2005-101475 (Patent Document 2)discloses a group III-V nitride based semiconductor substrate(specifically free-standing GaN substrate) having a substantiallyuniform distribution of the carrier concentration, and a method ofmanufacturing the semiconductor substrate. Although Japanese PatentLaying-Open No. 2005-101475 (Patent Document 2) discloses, regarding agroup III-V nitride based semiconductor substrate having a main surfacewhose plane orientation is (0001), that crystal growth is made flat toprovide a substantially uniform distribution of the carrierconcentration, Patent Document 2 does not disclose or suggest that thedistribution of the carrier concentration is made substantially flat fora group III-V nitride based semiconductor substrate having a mainsurface whose plane orientation is other than {0001}.

Further, Japanese Patent Laying-Open No. 2006-052102 (Patent Document 3)discloses a group III-V nitride based semiconductor substrate(specifically free-standing GaN substrate) having a substantiallyuniform distribution of the dislocation density, and a method ofmanufacturing the semiconductor substrate. Japanese Patent Laying-OpenNo. 2006-052102 (Patent Document 3) discloses, regarding a group III-Vnitride based semiconductor substrate having a main surface whose planeorientation is (0001), that a crystal is grown while concaves aregenerated on a growth interface, the growth interface is flattened, andthe crystal is further grown on the flattened growth interface, so thatthe dislocation density distribution is made substantially uniform.Patent Document 3, however, does not disclose or suggest that thedislocation density distribution is made substantially uniform for agroup III-V nitride based semiconductor substrate having a main surfacewhose plane orientation is other than {0001}.

Japanese Patent Laying-Open No. 2002-299741 (Patent Document 4)discloses a GaN single crystal substrate having a photoelasticitydistortion value of not more than 5×10⁻⁵ that is measured byphotoelasticity in a main surface of the substrate. Japanese PatentLaying-Open No. 2002-299741 (Patent Document 4) merely discloses,regarding a GaN single crystal substrate having a main surface whoseplane orientation is (0001), that a photoelasticity distortion value inthe main surface is not more than 5×10⁻⁵, and does not disclose orsuggest, regarding a GaN single crystal substrate having a main surfacewhose plane orientation is other than (0001) and (000-1), the maximumvalue and a variation of the photoelasticity distortion value in themain surface.

SUMMARY OF THE INVENTION

An object of the present invention is to solve the above-describedproblems and provide a GaN single crystal substrate suitable formanufacture of a GaN-based semiconductor device having superiorcharacteristics and a uniform distribution of characteristics,specifically a GaN single crystal substrate having a large area and amain surface whose plane orientation is other than (0001) and (000-1),and having at least one of a substantially uniform distribution of thecarrier concentration in the main surface, a substantially uniformdistribution of the dislocation density in the main surface, and a smallphotoelasticity distortion in the main surface that is a distortionmeasured by photoelasticity, and a method of manufacturing the GaNsingle crystal substrate. The present invention also has an object ofproviding a GaN-based semiconductor device having superiorcharacteristics and a uniform distribution of characteristics, andincluding such a GaN single crystal substrate and at least one GaN-basedsemiconductor layer formed on the main surface of the substrate, and amethod of manufacturing the GaN-based semiconductor device.

According to an aspect, the present invention is a GaN single crystalsubstrate having a main surface with an area of not less than 10 cm²,the main surface having a plane orientation inclined by not less than65° and not more than 85° with respect to one of a (0001) plane and a(000-1) plane, and the substrate has at least one of a substantiallyuniform distribution of a carrier concentration in the main surface, asubstantially uniform distribution of a dislocation density in the mainsurface, and a photoelasticity distortion value of not more than 5×10⁻⁵,the photoelasticity distortion value being measured by photoelasticityat an arbitrary point in the main surface when light is appliedperpendicularly to the main surface at an ambient temperature of 25° C.

In the GaN single crystal substrate according the above aspect of thepresent invention, a variation of the carrier concentration in the mainsurface may be within ±50% with respect to an average carrierconcentration in the main surface. Further, a distribution of a specificresistance in the main surface may be substantially uniform. Here, avariation of the specific resistance in the main surface may be within±50% with respect to an average specific resistance in the main surface.Further, an average specific resistance in the main surface may be notmore than 0.1 Ωcm.

In the GaN single crystal substrate according to the above aspect of thepresent invention, a variation of the dislocation density in the mainsurface may be within ±100% with respect to an average dislocationdensity in the main surface. Further, the dislocation density in themain surface may be not more than 5×10⁶ cm⁻².

In the GaN single crystal substrate according to the above aspect of thepresent invention, a variation of the photoelasticity distortion valuein the main surface may be within ±100% with respect to an average valueof the photoelasticity distortion value in the main surface.

In the GaN single crystal substrate according to the above aspect of thepresent invention, the plane orientation of the main surface may beinclined in <10-10> direction with respect to one of the (0001) planeand the (000-1) plane. Further, a half width of an x-ray diffractionpeak obtained by x-ray diffraction rocking curve measurement for one ofa combination of (0002) and (20-20) planes and a combination of (0002)and (22-40) planes may be not more than 300 arcsec in a whole of themain surface.

According to another aspect, the present invention is a method ofmanufacturing a GaN single crystal substrate according to the aboveaspect, including the steps of: preparing a GaN seed crystal substratehaving a main surface with an area of not less than 10 cm², the mainsurface having a plane orientation inclined by not less than 65° and notmore than 85° with respect to one of a (0001) plane and a (000-1) plane;growing a GaN single crystal on the main surface of the GaN seed crystalsubstrate; and forming the GaN single crystal substrate by cutting theGaN single crystal along a plane that is parallel with the main surfaceof the GaN seed crystal substrate.

According to still another aspect, the present invention is a GaN-basedsemiconductor device including a GaN single crystal substrate accordingto the above aspect, and at least one GaN-based semiconductor layerformed on the main surface of the GaN single crystal substrate.

According to a further aspect, the present invention is a method ofmanufacturing a GaN-based semiconductor device including the steps of:preparing a GaN single crystal substrate according to the above aspect;and growing at least one GaN-based semiconductor layer on the mainsurface of the GaN single crystal substrate.

The foregoing and other objects, features, aspects and advantages of thepresent invention will become more apparent from the following detaileddescription of the present invention when taken in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing an example of a GaN single crystalsubstrate according to an aspect of the present invention.

FIG. 2 is a schematic diagram showing an example of a method ofmeasuring a photoelasticity distortion value of a GaN single crystalsubstrate according to an aspect of the present invention.

FIG. 3 is a schematic diagram showing an example of a method ofmanufacturing a GaN single crystal substrate according to another aspectof the present invention. Here, (A) and (B) illustrate the step ofpreparing a GaN seed crystal substrate that includes the sub step ofcutting out a plurality of GaN mother crystal pieces from a GaN mothercrystal, and the sub step of arranging a plurality of GaN mother crystalpieces adjacently to each other in the lateral direction, (C)illustrates the step of growing a GaN single crystal, and (D)illustrates the step of forming a GaN single crystal substrate.

FIG. 4 is a schematic cross section showing another example of a methodof manufacturing a GaN single crystal substrate according to anotheraspect of the present invention. Here, (A) illustrates the step ofpreparing a GaN seed crystal substrate, (B) illustrates the step ofgrowing a GaN single crystal, and (C) illustrates the step of forming aGaN single crystal substrate.

FIG. 5 is a schematic diagram showing an example of the step ofpreparing a GaN seed crystal substrate in a further example of a methodof manufacturing a GaN single crystal substrate according to anotheraspect of the present invention. Here, (A) illustrates the sub step ofcutting out a plurality of GaN mother crystal pieces from a GaN mothercrystal, (B) illustrates the sub step of arranging a plurality of GaNmother crystal pieces adjacently to each other in the lateral direction,(C) illustrates the sub step of growing a GaN seed crystal, and (D)illustrates the sub step of forming a GaN seed crystal substrate.

FIG. 6 is a schematic cross section showing a further example of amethod of manufacturing a GaN single crystal substrate according toanother aspect of the present invention. Here, (A) illustrates the stepof preparing a GaN seed crystal substrate, (B) illustrates the step ofgrowing a GaN single crystal, and (C) illustrates the step of forming aGaN single crystal substrate.

FIG. 7 is a schematic diagram showing a state of inclination of a planeorientation of a main surface with respect to one of a (0001) plane anda (000-1) plane in a GaN single crystal substrate according to an aspectof the present invention. Here, (A) illustrates where the planeorientation of the main surface is {20-21}, (B) illustrates where theplane orientation of the main surface is {20-2-1}, (C) illustrates wherethe plane orientation of the main surface is {22-42}, and (D)illustrates where the plane orientation of the main surface is {22-4-2}.

FIG. 8 is a schematic cross section showing an example of a GaN-basedsemiconductor device according to a further aspect of the presentinvention.

FIGS. 9A and 9B are schematic diagrams showing a state of inclination ofa plane orientation of a main surface with respect to one of a (0001)plane and a (000-1) plane in a GaN single crystal substrate, and acombination of a (0002) plane and a (20-20) plane, and a combination ofa (0002) plane and a (22-40) plane for representing an x-ray diffractionrocking curve measurement.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

In crystallography, the plane orientation of a crystal plane isrepresented using notation such as (hkl) or (hkil) (Miller notation).The plane orientation of a crystal plane in a crystal of the hexagonalsystem such as group III nitride crystal that forms a GaN seed crystalsubstrate and a GaN single crystal substrate for example is representedby (hkil). Here, h, k, i, and l are each an integer called Miller index,and have a relation of i=−(h+k). A plane having the plane orientation(hkil) is called (hkil) plane. The direction perpendicular to the (hkil)plane (normal to (hkil) plane) is called [hkil] direction. {hkil}represents a family of plane orientations including (hkil) and planeorientations crystallographically equivalent thereto. <hkil> representsa family of directions including [hkil] and directionscrystallographically equivalent thereto.

Here, in a group III nitride crystal such as GaN seed crystal and GaNsingle crystal, group III element atom planes such as gallium (Ga) atomplanes and nitrogen (N) atom planes are arranged alternately in the<0001> direction, and therefore, the crystal has a polarity in the<0001> direction. In the present invention, crystal axes are defined sothat a group III element atom plane such as gallium atom plane is a(0001) plane, and a nitrogen atom plane is a (000-1) plane.

GaN Single Crystal Substrate Embodiment 1

Referring to FIGS. 1 and 2, a (GaN single crystal substrate 20 p in anembodiment of the present invention includes a main surface 20 pm havingan area of not less than 10 cm². The plane orientation of main surface20 pm is inclined by not less than 65° and not more than 85° withrespect to a plane 20 c that is one of a (0001) plane and a (000-1)plane. The substrate has at least one of a substantially uniformdistribution of the carrier concentration in main surface 20 pm, asubstantially uniform distribution of the dislocation density in mainsurface 20 pm, and a photoelasticity distortion value of not more than5×10⁻⁵ where the photoelasticity distortion value is measured byphotoelasticity at an arbitrary point in main surface 20 pm when light Lis applied perpendicularly to main surface 20 pm at an ambienttemperature of 25° C. GaN single crystal substrate 20 p in the presentembodiment is suitably used for manufacture of a GaN-based semiconductordevice having superior characteristics and a uniform distribution ofcharacteristics. A more specific description will be given below of GaNsingle crystal substrate 20 p in the present embodiment.

Embodiment 1A

Referring to FIG. 1, as to GaN single crystal substrate 20 p in thepresent embodiment, the area of main surface 20 pm is not less than 10cm², the plane orientation of main surface 20 pm is inclined by not lessthan 65° and not more than 85° with respect to plane 20 c that is one ofa (0001) plane and a (000-1) plane, and the distribution of the carrierconcentration in main surface 20 pm is substantially uniform.

GaN single crystal substrate 20 p in the present embodiment has a largearea of main surface 20 pm of 10 cm² or more. Further, the planeorientation of main surface 20 pm is inclined by an inclination angle αof not less than 65° and not more than 85° with respect to plane 20 cthat is one of a (0001) plane and a (000-1) plane, and therefore, blueshift of light emission from a GaN-based semiconductor device using sucha GaN single crystal substrate 20 p is suppressed and degradation inluminous efficacy is thus suppressed. In view of this, the planeorientation of main surface 20 pm is inclined preferably by inclinationangle α of not less than 70° and not more than 80° with respect to plane20 c that is one of a (0001) plane and a (000-1) plane, and morepreferably by inclination angle α of not less than 72° and not more than78° with respect thereto. Further, the distribution of the carrierconcentration in main surface 20 pm is substantially uniform, andtherefore, in a GaN-based semiconductor device using such a GaN singlecrystal substrate 20 p, the distribution of device characteristics in amain surface of the device is substantially uniform.

Regarding GaN single crystal substrate 20 p in the present embodiment,the fact that the distribution of the carrier concentration in mainsurface 20 pm is substantially uniform means that the distribution ofdevice characteristics in a main surface of a GaN-based semiconductordevice using the GaN single crystal substrate is substantially uniform,and is represented for example by a variation within ±50% of the carrierconcentration in main surface 20 pm, with respect to an average carrierconcentration in main surface 20 pm. In order to further equalize thedistribution of device characteristics in the main surface of theGaN-based semiconductor device, it is preferable that a variation of thecarrier concentration in main surface 20 pm is within ±30% with respectto the average carrier concentration in main surface 20 pm. Here, thecarrier concentration in main surface 20 pm of GaN single crystalsubstrate 20 p may be measured for example by the van der Pauw methodalong a two-dimensional direction and at a pitch of 2 mm in main surface20 pm.

For GaN single crystal substrate 20 p in the present embodiment, inorder to equalize the distribution of device characteristics, it ispreferable that the distribution of the specific resistance in mainsurface 20 pm is substantially uniform. Here, the fact that thedistribution of the specific resistance in main surface 20 pm of GaNsingle crystal substrate 20 p is substantially uniform means that thedistribution of device characteristics in a main surface of a GaN-basedsemiconductor device using the GaN single crystal substrate issubstantially uniform, and is represented for example by a variationwithin ±50% of the specific resistance in main surface 20 pm, withrespect to an average specific resistance in the main surface. In orderto further equalize the distribution of device characteristics in themain surface of the GaN-based semiconductor device, a variation of thespecific resistance in main surface 20 pm of GaN single crystalsubstrate 20 p is preferably within ±30% with respect to the averagespecific resistance in main surface 20 pm. Further, in order to enhancethe electrical conductivity of the GaN-based semiconductor device, it ispreferable that the average specific resistance in main surface 20 pm ofGaN single crystal substrate 20 p is not more than 0.1 Ωcm. Here, thespecific resistance in main surface 20 pm of GaN single crystalsubstrate 20 p may be measured for example by the van der Pauw methodalong a two-dimensional direction and at a pitch of 2 mm in main surface20 pm.

For GaN single crystal substrate 20 p in the present embodiment, inorder to achieve stable epitaxial growth of a GaN-based semiconductorlayer of high crystallinity, it is preferable that the direction ofinclination of the plane orientation of main surface 20 pm with respectto plane 20 c that is one of a (0001) plane and a (000-1) plane is the<10> direction. For a similar purpose, it is preferable that the halfwidth of an x-ray diffraction peak obtained by x-ray diffraction rockingcurve measurement for one of a combination of (0002) and (20-20) planesand a combination of (0002) and (22-40) planes is not more than 300arcsec over the whole main surface 20 pm, these planes represented inFIGS. 9A and 9B. A smaller half width of the x-ray diffraction peakrepresents higher crystallinity.

For GaN single crystal substrate 20 p where the plane orientation ofmain surface 20 pm is {h0kl} (h, k and l are each an integer other than0), diffraction crystal planes for the x-ray diffraction rocking curvemeasurement may be a (0002) plane and a (20-20) plane, or may be a(0002) plane and a (22-40) plane. Likewise, for GaN single crystalsubstrate 20 p where the plane orientation of main surface 20 pm is{hikl} (h, k, i, and l are each an integer other than 0), diffractioncrystal planes for the x-ray diffraction rocking curve measurement maybe a (0002) plane and a (20-20) plane, or may be a (0002) plane and a(22-40) plane. X-ray diffraction rocking curve measurement in the wholeof main surface 20 pm of GaN single crystal substrate 20 p may beperformed for example along a two-dimensional direction and at a pitchof 2 mm in main surface 20 pm and with an x-ray irradiation area of 1mm².

Embodiment 1B

Referring to FIG. 1, as to GaN single crystal substrate 20 p in thepresent embodiment, the area of main surface 20 pm is not less than 10cm², the plane orientation of main surface 20 pm is inclined by not lessthan 65° and not more than 85° with respect to plane 20 c that is one ofa (0001) plane and a (000-1) plane, and the distribution of thedislocation density in main surface 20 pm is substantially uniform.

GaN single crystal substrate 20 p in the present embodiment has a largearea of main surface 20 pm of 10 cm² or more. Further, the planeorientation of main surface 20 pm is inclined by an inclination angle atof not less than 65° and not more than 85° with respect to plane 20 cthat is one of a (0001) plane and a (000-1) plane, and therefore, blueshift of light emission from a GaN-based semiconductor device using sucha GaN single crystal substrate 20 p is suppressed and degradation inluminous efficacy is thus suppressed. In view of this, the planeorientation of main surface 20 pm is inclined preferably by inclinationangle α of not less than 70° and not more than 80° with respect to plane20 c that is one of a (0001) plane and a (000-1) plane, and morepreferably by inclination angle α of not less than 72° and not more than78° with respect thereto. Further, the distribution of the dislocationdensity in main surface 20 pm is substantially uniform, and therefore,in a GaN-based semiconductor device using such a GaN single crystalsubstrate 20 p, the distribution of device characteristics in a mainsurface of the device is substantially uniform.

Regarding GaN single crystal substrate 20 p in the present embodiment,the fact that the distribution of the dislocation density in mainsurface 20 pm is substantially uniform means that the distribution ofdevice characteristics in a main surface of a GaN-based semiconductordevice using the GaN single crystal substrate is substantially uniform,and is represented for example by a variation within ±100% of thedislocation density in main surface 20 pm of GaN single crystalsubstrate 20 p, with respect to an average dislocation density in mainsurface 20 pm In order to further equalize the distribution of devicecharacteristics in the main surface of the GaN-based semiconductordevice, a variation of the dislocation density in main surface 20 pm ofGaN single crystal substrate 20 p is preferably within −100% to +70%with respect to the average dislocation density in main surface 20 pm,and more preferably within −100% to +50% with respect thereto. Here, thedislocation density in main surface 20 pm of GaN single crystalsubstrate 20 p may be measured for example by the CL(cathodoluminescence) method, along a two-dimensional direction and at apitch of 2 mm in main surface 20 pm, for a measurement area of 100μm×100 μm.

For GaN single crystal substrate 20 p in the present embodiment, inorder to epitaxially grow a GaN-based semiconductor layer of highcrystallinity, the dislocation density in main surface 20 pm ispreferably not more than 5×10⁶ cm⁻² at a maximum dislocation density,and more preferably not more than 1×10⁻⁶ cm⁻².

For GaN single crystal substrate 20 p in the present embodiment, inorder to achieve stable epitaxial growth of a GaN-based semiconductorlayer of high crystallinity, it is preferable that the direction ofinclination of the plane orientation of main surface 20 pm with respectto plane 20 c that is one of a (0001) plane and a (000-1) plane is the<10-10> direction. For a similar purpose, it is preferable that the halfwidth of an x-ray diffraction peak obtained by x-ray diffraction rockingcurve measurement for one of a combination of (0002) and (20-20) planesand a combination of (0002) and (22-40) planes is not more than 300arcsec over the whole main surface 20 pm, these planes represented inFIGS. 9A and 9B. A smaller half width of the x-ray diffraction peakrepresents higher crystallinity.

For GaN single crystal substrate 20 p where the plane orientation ofmain surface 20 pm is (h0kl) (h, k and l are each an integer other than0), diffraction crystal planes for the x-ray diffraction rocking curvemeasurement may be a (0002) plane and a (20-20) plane, or may be a(0002) plane and a (22-40) plane. Likewise, for GaN single crystalsubstrate 20 p where the plane orientation of main surface 20 pm is{hikl} (h, k, i, and l are each an integer other than 0), diffractioncrystal planes for the x-ray diffraction rocking curve measurement maybe a (0002) plane and a (20-20) plane, or may be a (0002) plane and a(22-40) plane X-ray diffraction rocking curve measurement for the entiremain surface 20 pm of GaN single crystal substrate 20 p may be performedfor example along a two-dimensional direction and at a pitch of 2 mm inmain surface 20 pm and with an x-ray irradiation area of 1 mm².

Embodiment 1C

Referring to FIG. 1, as to GaN single crystal substrate 20 p in anembodiment of the present invention, the area of main surface 20 pm isnot less than 10 cm², the plane orientation of main surface 20 pm isinclined by not less than 65° and not more than 85° with respect toplane 20 c that is one of a (0001) plane and a (000-1) plane, and aphotoelasticity distortion value is not more than 5×10⁻⁵ where thephotoelasticity distortion value is measured by photoelasticity at anarbitrary point in main surface 20 pm when light is appliedperpendicularly to main surface 20 pm at an ambient temperature of 25°C.

GaN single crystal substrate 20 p in the present embodiment has a largearea of main surface 20 pm of 10 cm² or more. Further, the planeorientation of main surface 20 pm is inclined by an inclination angle αof not less than 65° and not more than 85° with respect to plane 20 cthat is one of a (0001) plane and a (000-1) plane, and therefore, blueshift of light emission from a GaN-based semiconductor device using sucha GaN single crystal substrate 20 p is suppressed and degradation inluminous efficacy is thus suppressed. In view of this, the planeorientation of main surface 20 pm is inclined preferably by inclinationangle α of not less than 70° and not more than 80° with respect to plane20 c that is one of a (0001) plane and a (000-1) plane, and morepreferably by inclination angle α of not less than 72° and not more than80° with respect thereto. Further, the photoelasticity distortion valueis not more than 5×10⁻⁵ that is measured by photoelasticity at anarbitrary point in main surface 20 pm when light is appliedperpendicularly to main surface 20 pm at an ambient temperature of 25°C., and therefore, for a GaN-based semiconductor device using such a GaNsingle crystal substrate 20 p, a large number of effects are expectedincluding, for example, the effect that cracks are unlikely to begenerated during production of the device, the effect that warp isreduced and the temperature uniformity is improved in epitaxial growthof a GaN-based semiconductor layer, the effect that the cleavagecharacteristic of the device is improved, and the effect that the polishquality of the substrate and the device is improved. In view of this,the photoelasticity distortion value is more preferably not more than2×10⁻⁵ and still more preferably not more than 1×10⁺⁵.

Here, photoelasticity refers to the phenomenon that internal stress σ ofan elastic object causes different refractive indices of light, namelyanisotropy of internal stress σ causes birefringence to be generated inthe object. It is supposed that there are three principal axes (x axis,y axis, z axis) for stress that are orthogonal to each other, and theaxis of direction perpendicular to the main surface of the GaN singlecrystal substrate is the z axis. Referring to FIG. 2, light L ofwavelength λ (monochromatic light of wavelength λ, or polychromatic orwhite light of peak wavelength λ) is applied, via a polarizer 30 and aλ/4 plate 40, perpendicularly to main surface 20 pm of GaN singlecrystal substrate 20 p of thickness t, and the light transmitted throughthe GaN single crystal substrate is observed via a λ/4 plate 50 and ananalyzer 60. Then, two components of the polarized light that havedifferent phases and are orthogonal to each other are observed. Here,the λ/4 plate is a device having a function of shifting (retarding forexample) the phase of light having two components of perpendicularpolarization planes.

Phase difference δ between the two polarized light components asobserved is expressed by the following equation (1), with respectiveinternal stresses σ_(x) and σ_(y) in the x-axis and z-axis directions,and respective changes Δn_(x) and Δn_(y) of the refractive index of thelight components having polarization planes in these directions, usingphotoelasticity coefficient C that is a rate of change of the refractiveindex caused by a unit stress increase, light wavelength λ, andthickness t of the GaN single crystal substrate:δ=2πt(Δn _(x) −Δn _(y))/λ=2πtC(σ_(x)−σ_(y))/λ  (1)where Δn_(x)=Cσ_(x) and Δn_(y)=Cσ_(y). Here, the photoelasticitydistortion value is defined by C (σ_(x)−σ_(y)) in equation (1). Thepolarization plane of the polarizer is made parallel with one of the xaxis and the y axis that are principal axes of the internal stress, andthe quantity of transmitted light when the polarization plane of theanalyzer is made orthogonal to the polarization plane of the polarizer,and the quantity of transmitted light when the polarization plane of theanalyzer is made parallel with the polarization plane of the polarizerare measured, phase difference δ is determined from a value representingthe ratio between the measured quantities, and further, photoelasticitydistortion value C(σ_(x)−σ_(y)) is determined from equation (1). Itshould be noted that photoelasticity coefficient C is a constantdetermined depending on the type and structure of the crystal and theambient temperature for measurement, and is the same value for the samecrystal type, the same crystal structure and the same ambienttemperature for measurement. Details of the method for determiningphotoelasticity distortion value C (σ_(x)−σ_(y)) is disclosed inJapanese Patent Laying-Open No. 2002-299741.

For GaN single crystal substrate 20 p in the present embodiment, inorder to achieve stable epitaxial growth of a GaN-based semiconductorlayer of high crystallinity, it is preferable that the direction ofinclination of the plane orientation of main surface 20 pm with respectto plane 20 c that is one of a (0001) plane and a (000-1) plane is the<10-10> direction. For growth of a GaN-based semiconductor layer of highcrystallinity, a variation of the photoelasticity distortion value inmain surface 20 pm is preferably within ±100% with respect to an averageof the photoelasticity distortion value in main surface 20 pm, and ismore preferably −100% to +85% with respect thereto. Here, measurement ofthe photoelasticity distortion value at an arbitrary point in mainsurface 20 pm of GaN single crystal substrate 20 p may be done along atwo-dimensional direction and at a pitch of 2 mm in main surface 20 pm.

Method of Manufacturing GaN Single Crystal Substrate Embodiment 2

Referring to FIGS. 3 to 6, a method of manufacturing a GaN singlecrystal substrate in another embodiment of the present invention is amethod of manufacturing GaN single crystal substrate 20 p in Embodiment1, and includes the step of preparing a GaN seed crystal substrate 10 phaving a main surface 10 pm with an area of not less than 10 cm², mainsurface 10 pm having a plane orientation inclined by not less than 65°and not more than 85° with respect to plane 1 c, 10 c that is one of a(0001) plane and a (000-1) plane, the step of growing a GaN singlecrystal 20 on main surface 10 pm of GaN seed crystal substrate 10 p, andthe step of forming GaN single crystal substrate 20 p by cutting GaNsingle crystal 20 along a plane located parallel with main surface 10 pmof GaN seed crystal substrate 100 p. The method of manufacturing a GaNsingle crystal substrate in the present embodiment provides the GaNsingle crystal substrate suitably used for manufacture of a GaN-basedsemiconductor device having superior characteristics and a uniformdistribution of characteristics. A more specific description will begiven of a method of manufacturing a GaN single crystal substrate inEmbodiments 1A, 1B, and 1C each

Embodiment 2A

Referring to FIGS. 3 and 4, a method of manufacturing a GaN singlecrystal substrate in the present embodiment is a method of manufacturingGaN single crystal substrate 20 p in Embodiment 1A, and includes thestep of preparing GaN seed crystal substrate 10 p having main surface 10pm with an area of not less than 10 cm², main surface 10 pm having aplane orientation inclined by not less than 65° and not more than 85°with respect to plane c, 10 c that is one of a (0001) plane and a(000-1) plane (FIG. 3 (A) to (B), FIG. 4 (A)), the step of growing GaNsingle crystal 20 on main surface 10 pm of GaN seed crystal substrate 10p (FIG. 3 (C), FIG. 4 (B)), and the step of forming the GaN singlecrystal substrate by cutting GaN single crystal 20 along planes 20 u, 20v that are parallel with main surface 10 pm of GaN seed crystalsubstrate 10 p (FIG. 3 (D), FIG. 4 (C)). The method of manufacturing aGaN single crystal substrate in the present embodiment includes theabove-described steps so that the GaN single crystal substrate inEmbodiment 1A can be manufactured efficiently

Example I of Embodiment 2A

Referring to FIG. 3, an example of the method of manufacturing a GaNsingle crystal substrate in the present embodiment (hereinafter ExampleI) will be described.

Referring to FIGS. 3 (A) and (B), in Example I, the step of preparingGaN seed crystal substrate 10 p includes the sub step of cutting out,from a GaN mother crystal 1, a plurality of GaN mother crystal pieces 1p each having a main surface 1 pm with plane orientation inclined byinclination angle α of not less than 65° and not more than 85° withrespect to plane 1 c that is one of a (0001) plane and a (000-1) plane(FIG. 3 (A)), and the sub step of forming GaN seed crystal substrate 10p having main surface 10 pm with an area of not less than 10 cm², mainsurface 10 pm having a plane orientation inclined by an inclinationangle α of not less than 65° and not more than 85° with respect to plane1 c that is one of a (0001) plane and a (000-1) plane, GaN seed crystalsubstrate 10 p being formed by arranging a plurality of GaN mothercrystal pieces 1 p adjacently to each other in the lateral direction, sothat respective main surfaces 1 pm of the mother crystal pieces areparallel to each other and respective [0001] directions of the mothercrystal pieces are parallel to each other (FIG. 3 (B)).

Referring first to FIG. 3 (A), in the sub step of cutting out aplurality of GaN mother crystal pieces 1 p, a plurality of GaN mothercrystal pieces 1 p are cut out from GaN mother crystal 1 along a planethat is parallel with the plane orientation {hkil}inclined byinclination angle α of not less than 65° and not more than 85° withrespect to plane 1 c that is one of a (0001) plane and a (000-1) planeof GaN mother crystal 1 (along a plane perpendicular to the <hkil>direction). Here, inclination angle α can be measured by the x-raydiffractometry.

GaN mother crystal 1 used in the above step is not limited to aparticular one, and may be any that is manufactured by a commonly usedmethod, namely by any of vapor phase methods such as HVPE and MOCVD, andliquid phase methods such as flux method, to cause crystal growth on amain surface of a sapphire substrate having the main surface of a (0001)plane or GaAs substrate having the main surface of a (111) A plane, forexample. Therefore, while GaN mother crystal 1 is not limited to aparticular one, the mother crystal commonly has a main surface of a(0001) plane. In order to reduce the dislocation density and enhance thecrystallinity, this GaN mother crystal 1 is preferably grown by thefacet growth method having a feature that facets are formed at a surfacewhere a crystal grows (crystal growth surface) and the crystal is grownwithout burying the facets, as disclosed in Japanese Patent Laying-OpenNo. 2001-102307.

The method of cutting out a plurality of GaN mother crystal pieces 1 pfrom GaN mother crystal 1 is not limited to a particular one, and mayuse any of various means such as wire saw, inner peripheral blade, outerperipheral blade, or laser, for example.

In order to grow GaN single crystal 20 of high crystallinity, averageroughness Ra of each of main surfaces 1 pm and side surfaces of aplurality of GaN mother crystal pieces 1 p is preferably not more than50 nm and more preferably not more than 5 nm Average roughness Ra ofsurfaces refers to arithmetic average roughness Ra defined by JIS B0601: 2001, and specifically to a value determined by removing from aroughness curve a portion of a reference length along the direction inwhich an average line extends, calculating the sum of distances from theaverage line to the roughness curve in the removed portion (respectiveabsolute values of the deviations), and dividing the sum by thereference length. Average roughness Ra of a surface can be measured bymeans of an AFM (atomic force microscope) or the like.

In order that average roughness Ra of each of main surfaces 1 pm andside surfaces of a plurality of GaN mother crystal pieces 1 p may bepreferably not more than 50 nm and more preferably not more than 5 nm,it is preferable that a plurality of cut-out GaN mother crystal pieces 1p have respective main surfaces 1 pm and side surfaces that are groundand/or polished. Polishing includes mechanical polishing, CMP (chemicalmechanical polishing) and the like.

Then, referring to FIG. 3 (B), in the sub step of forming GaN seedcrystal substrate 10 p, a plurality of cut-out GaN mother crystal pieces1 p are arranged adjacently to each other in the lateral direction sothat respective main surfaces 1 pm of the mother crystal pieces areparallel to each other and respective [0001] directions thereof areidentical. Thus, GaN seed crystal substrate 10 p is formed that has mainsurface 10 pm with an area of not less than 10 cm² and with the planeorientation inclined by not less than 65° and not more than 85° withrespect to plane 1 c that is one of a (0001) plane and a (000-1) plane.

Regarding a plurality of GaN mother crystal pieces 1 p, if respectiveangles formed between main surfaces 1 pm and the crystal axis are notuniform in main surface 10 pm of GaN seed crystal substrate 10 p formedin the above-described manner, the chemical composition of the GaNsingle crystal grown on main surface 10 pm of GaN seed crystal substrate10 p is not uniform within a plane that is parallel with main surface 10pm of GaN seed crystal substrate 10 p. Therefore, a plurality of GaNmother crystal pieces 1 p are arranged laterally so that respective mainsurfaces 1 pm of these mother crystal pieces are parallel to each other.As long as respective main surfaces 1 pm of these mother crystal piecesare parallel to each other, the main surfaces may not necessarily be onthe same plane. Level difference ΔT (not shown) between respective mainsurfaces 1 pm of two GaN mother crystal pieces 1 p adjacent to eachother, however, is preferably not more than 0.1 mm and more preferablynot more than 0.01 mm.

Further, regarding a plurality of GaN mother crystal pieces 1 p, inorder to have the same crystal orientations of these mother crystalpieces and thereby achieve more uniform crystal growth, the GaN mothercrystal pieces are arranged laterally so that respective [0001]directions of these mother crystal pieces are identical. A plurality ofGaN mother crystal pieces 1 p are also arranged adjacently to eachother, because a gap between substrates, if any, deteriorates thecrystallinity of a crystal grown on the gap.

Then, referring to FIG. 3 (C), in the step of growing GaN single crystal20 on main surface 10 pm of GaN seed crystal substrate 10 p, the methodof growing GaN single crystal 20 is not limited to a particular one. Inorder to epitaxially grow the GaN single crystal, preferably any ofvapor phase methods such as HVPE and MOCVD and liquid phase methods suchas flux method is used. Among the crystal growth methods, the HVPEmethod is preferable because it provides a high crystal growth rate.

When GaN single crystal 20 has been grown on main surface 10 pm of GaNseed crystal substrate 10 p, a crystal growth surface 20 g of GaN singlecrystal 20 is macroscopically parallel with main surface 10 pm of GaNseed crystal substrate 10 p. Microscopically, however, a plurality offacets 20 fa, 20 fb that are not in parallel with main surface 10 pm ofGaN seed crystal substrate 10 p are formed at crystal growth surface 20g. Such a plurality of facets 20 fa, 20 fb have respective planeorientations different from each other. Namely, GaN single crystal 20 isgrown with crystal growth surface 20 g including facet surfaces 20 fa,20 fb having respective plane orientations different from each other.Here, since facet 20 fa and facet 20 fb are different in planeorientation, respective concentrations of impurities taken from thesefacets are different from each other. Therefore, in GaN single crystal20 grown on main surface 10 pm of GaN seed crystal substrate 10 p, avariation in carrier concentration is generated in a plane that isparallel with main surface 10 pm of GaN seed crystal substrate 10 p.

At this time, if the inclination of the plane orientation of mainsurface 10 pm of GaN seed crystal substrate 10 p with respect to plane 1c that is one of a (0001) plane and a (000-1) plane is small, forexample, if angle α of the inclination is smaller than 65°, crystalgrowth surface 20 g of GaN single crystal 20 grown on this main surface10 pm is accordingly accompanied by facet 20 fa having the planeorientation (0001) or (000-1) and facet 20 fb having a plane orientationdifferent from facet 20 fa. Here, the concentration of impurities takenfrom facet 20 fa with the plane orientation (0001) or (000-1) issignificantly different from the concentration of impurities taken fromfacet 20 fb with a plane orientation other than (0001) and (000-1).Therefore, in GaN single crystal 20 grown on main surface 10 pm of GaNseed crystal substrate 10 p where the inclination of the planeorientation of main surface 10 pm is small with respect to plane 1 cthat is one of a (0001) plane and a (000-1) plane, the carrierconcentration in a plane that is parallel with main surface 10 pm of GaNseed crystal substrate 10 p varies to a great extent

In contrast, if the inclination of the plane orientation of main surface10 pm of GaN seed crystal substrate 10 p with respect to plane 1 c thatis one of a (0001) plane and a (000-1) plane is large and close to theright angle, for example, if angle α of the inclination is larger than85°, facets 20 fb having the plane orientation perpendicular to (0001)are predominantly generated at crystal growth surface 20 g of GaN singlecrystal 20 grown on main surface 10 pm. Therefore, GaN single crystal 20as grown is partially polycrystallized, resulting in a crack in GaNsingle crystal 20.

In view of the above, in order to manufacture GaN single crystalsubstrate 20 p having a substantially uniform distribution of thecarrier concentration in main surface 20 pm, it is required that theplane orientation of main surface 10 pm of GaN seed crystal substrate 10p has inclination angle α of not less than 65° and not more than 85°with respect to plane 1 c that is one of a (0001) plane and a (000-1)plane, the inclination angle is preferably not less than 70° and notmore than 80° and more preferably not less than 72° and not more than78°.

Referring next to FIGS. 3 (C) and (D), in the step of forming GaN singlecrystal substrate 20 p by cutting GaN single crystal 20 along planes 20u, 20 v that are parallel with main surface 10 pm of GaN seed crystalsubstrate 10 p, the method of cutting out GaN single crystal substrate20 p from GaN single crystal 20 is not limited to a particular one, andmay use any of various means such as wire saw, inner peripheral blade,outer peripheral blade, or laser, for example. Here, the plane alongwhich GaN single crystal substrate 20 p is cut out may be displaced fromthe position parallel with the main surface of GaN seed crystalsubstrate 10 p as appropriate according to the purpose.

In order to grow a GaN-based semiconductor layer of high crystallinity,average roughness Ra of main surface 20 pm of GaN single crystalsubstrate 20 p is preferably not more than 50 nm and more preferably notmore than 5 nm. The definition and the way to measure average roughnessRa of the surface are similar to the above-described ones. In order thataverage roughness Ra of main surface 20 pm of GaN single crystalsubstrate 20 p may be preferably not more than 50 nm and more preferablynot more than 5 nm, it is preferable that cut-out GaN single crystalsubstrate 20 p has main surface 20 pm and side surface that are groundand/or polished. Polishing includes mechanical polishing, CMP (chemicalmechanical polishing) and the like.

Through the above-described steps, GaN single crystal substrate 20 p isobtained that has main surface 20 pm with an area of not less than 10cm² and with the plane orientation inclined by not less than 65° and notmore than 85° with respect to plane 20 c that is one of a (0001) planeand a (000-1) plane, and has a substantially uniform distribution of thecarrier concentration in main surface 20 pm (for example, a variation ofthe carrier concentration in main surface 20 pm is within ±50% withrespect to an average carrier concentration in this main surface 20 pm).

Example II of Embodiment 2A

Referring to FIG. 4, another example of the method of manufacturing aGaN single crystal substrate in the present embodiment (hereinafterExample II) will be described.

With reference to FIG. 4 (A), in Example II, in the step of preparingGaN seed crystal substrate 10 p, the GaN single crystal substratemanufactured in above-described Example I is prepared. Namely, as GaNseed crystal substrate 10 p, the GaN single crystal substratemanufactured in above-described Example I is used. The GaN singlecrystal substrate manufactured in Example I above has a main surfacewith an area of not less than 10 cm² and with the plane orientationinclined by not less than 65° and not more than 85° with respect toplane 10 c that is one of a (0001) plane and a (000-1) plane, andfurther has a uniform distribution of the carrier concentration in themain surface (for example, a variation of the carrier concentration inthe main surface is within ±50% with respect to an average carrierconcentration in this main surface). Thus, the GaN single crystalsubstrate in Embodiment 1A can be manufactured.

Next, referring to FIG. 4 (B), the step of growing GaN single crystal 20on main surface 10 pm of GaN seed crystal substrate 10 p is similar tothat in Example I above except that GaN seed crystal substrate 10 p isformed of one GaN single crystal substrate instead of a plurality of GaNmother crystal pieces.

Next, referring to FIGS. 4 (B) and (C), the step of forming GaN singlecrystal substrate 20 p by cutting GaN single crystal 20 along a planelocated parallel with main surface 10 pm of GaN seed crystal substrate10 p is similar to that in Example I above. Here, the plane along whichGaN single crystal substrate 20 p is cut out may be displaced from theposition parallel with the main surface of GaN seed crystal substrate 10p as appropriate according to the purpose.

Through the above-described steps, GaN single crystal substrate 20 p isobtained that has main surface 20 pm with an area of not less than 10cm² and with the plane orientation inclined by not less than 65° and notmore than 85° with respect to plane 20 c that is one of a (0001) planeand a (000-1) plane, and has a substantially uniform distribution of thecarrier concentration in main surface 20 pm (for example, a variation ofthe carrier concentration in main surface 20 pm is within ±50% withrespect to an average carrier concentration in this main surface 20 pm).

If a substrate having a main surface with the plane orientation inclinedby inclination angle α of not less than 65° and not more than 85° withrespect to one of a (0001) plane and a (000-1) plane and with a largearea of not less than 10 cm² can be cut out from a thick GaN mothercrystal, the substrate may be used as the GaN seed crystal substrate. Asfor this method, however, it is very difficult and troublesome toproduce a GaN seed crystal substrate of a large area. Therefore, likeExample I in Embodiment 2A above, it is important to cut out a pluralityof GaN mother crystal pieces from a single GaN mother crystal andarrange the plurality of GaN mother crystal pieces to form a GaN seedcrystal substrate.

Embodiment 2B

Referring to FIGS. 5 and 6, a method of manufacturing a GaN singlecrystal substrate in the present embodiment is a method of manufacturingGaN single crystal substrate 20 p in Embodiment 1B or 1C, and includesthe step of preparing GaN seed crystal substrate 10 p having mainsurface 10 pm with an area of not less than 10 cm², main surface 10 pmhaving a plane orientation inclined by not less than 65° and not morethan 85° with respect to plane 1 c, 10 c that is one of a (0001) planeand a (000-1) plane (FIG. 5 (A) to (D), FIG. 6 (A)), the step of growingGaN single crystal 20 on main surface 10 pm of GaN seed crystalsubstrate 10 p (FIG. 6 (B)), and the step of forming a GaN singlecrystal substrate 20 p by cutting GaN single crystal 20 along planes 20u, 20 v that are parallel with main surface 10 pm of GaN seed crystalsubstrate 10 p (FIG. 6 (C)). The method of manufacturing a GaN singlecrystal substrate in the present embodiment includes the above-describedsteps so that the GaN single crystal substrate in Embodiment 1B or 1Ccan be manufactured efficiently.

Step of Preparing GaN Seed Crystal Substrate

Referring to FIG. 5, while the step of preparing a GaN seed crystalsubstrate in the present embodiment is not limited to a particular one,the step includes for example the sub step of cutting out a plurality ofGaN mother crystal pieces from a GaN mother crystal (FIG. 5 (A)), thesub step of arranging a plurality of GaN mother crystal piecesadjacently to each other in the lateral direction (FIG. 5 (B)), the substep of growing a GaN seed crystal on main surfaces of a plurality ofGaN mother crystal pieces (FIG. 5 (C)), and the sub step of forming aGaN seed crystal substrate from the GaN seed crystal (FIG. 5 (D)).

First, referring to FIG. 5 (A), in the sub step of cutting out aplurality of GaN mother crystal pieces 1 p, a plurality of GaN mothercrystal pieces ip are cut out from GaN mother crystal 1 along planesthat are parallel with the plane orientation {hkil} inclined byinclination angle α of not less than 65° and not more than 85° withrespect to plane 1 c that is one of a (0001) plane and a (000-1) planeof GaN mother crystal 1 (along planes perpendicular to the <hkil>direction). With this sub step, a plurality of GaN mother crystal pieces1 p each having main surface 1 pm with the plane orientation inclined byinclination angle α of not less than 65° and not more than 85° withrespect to plane 1 c that is one of a (0001) plane and a (000-1) planeis obtained. Here, inclination angle α can be measured by the x-raydiffractometry.

GaN mother crystal 1 used in the above sub step is not limited to aparticular one, and may be any that is manufactured by a commonly usedmethod, namely by any of vapor phase methods such as HVPE and MOCVD, andliquid phase methods such as flux method, to cause crystal growth on amain surface of a sapphire substrate having the main surface of the(0001) plane or GaAs substrate having the main surface of the (111) Aplane, for example. Therefore, while GaN mother crystal 1 is not limitedto a particular one, the mother crystal commonly has a main surface ofthe (0001) plane. In order to reduce the dislocation density and enhancethe crystallinity, this GaN mother crystal 1 is preferably grown by thefacet growth method having a feature that facets are formed at a surfacewhere the crystal grows (crystal growth surface) and the crystal isgrown without burying the facets, as disclosed in Japanese PatentLaying-Open No. 2001-102307.

The method of cutting out a plurality of GaN mother crystal pieces 1 pfrom GaN mother crystal 1 is not limited to a particular one, and mayuse any of various means such as wire saw, inner peripheral blade, outerperipheral blade, or laser, for example.

In order to grow GaN seed crystal 10 of high crystallinity, averageroughness Ra of each of main surfaces 1 pm and side surfaces of aplurality of GaN mother crystal pieces 1 p is preferably not more than50 nm and more preferably not more than 5 nm. Average roughness Ra ofsurfaces refers to arithmetic average roughness Ra defined by JIS B0601: 2001, and specifically to a value determined by removing from aroughness curve a portion of a reference length along the direction inwhich an average line extends, calculating the sum of distances from theaverage line to the roughness curve in the removed portion (respectiveabsolute values of the deviations), and dividing the sum by thereference length. Average roughness Ra of surfaces can be measured bymeans of an AFM (atomic force microscope) or the like.

In order that average roughness Ra of each of main surfaces 1 pm andside surfaces of a plurality of GaN mother crystal pieces 1 p may bepreferably not more than 50 nm and more preferably not more than 5 nm,it is preferable that a plurality of cut-out GaN mother crystal pieces 1p have respective main surfaces 1 pm and side surfaces that are groundand/or polished. Polishing includes mechanical polishing, CMP (chemicalmechanical polishing) and the like.

Then, referring to FIG. 5 (B), in the sub step of arranging a pluralityof GaN mother crystal pieces adjacently to each other in the lateraldirection, a plurality of cut-out GaN mother crystal pieces 1 p arearranged adjacently to each other in the lateral direction so thatrespective main surfaces 1 pm of the mother crystal pieces are parallelto each other and respective [0001] directions thereof are identical.

Regarding a plurality of GaN mother crystal pieces 1 p, if respectiveangles formed between main surfaces 1 pm and the crystal axis are notuniform in main surfaces 1 pm of the mother crystal pieces, the chemicalcomposition of a GaN seed crystal grown on main surfaces 1 pm of themother crystal pieces is not uniform within a plane that is parallelwith main surfaces 1 pm of the mother crystal pieces. Therefore, aplurality of GaN mother crystal pieces 1 p are arranged laterally sothat respective main surfaces 1 pm of these mother crystal pieces areparallel to each other. As long as respective main surfaces 1 pm ofthese mother crystal pieces are parallel to each other, the mainsurfaces may not necessarily be on the same plane. Level difference ΔT(not shown) between respective main surfaces 1 pm of two GaN mothercrystal pieces 1 p adjacent to each other, however, is preferably notmore than 0.1 mm and more preferably not more than 0.01 mm.

Further, regarding a plurality of GaN mother crystal pieces 1 p, inorder to have the same crystal orientations of these mother crystalpieces and thereby achieve more uniform crystal growth, the GaN mothercrystal pieces are arranged laterally so that respective [0001]directions of these mother crystal pieces are identical. A plurality ofGaN mother crystal pieces 1 p are also arranged adjacently to eachother, because a gap between substrates, if any, deteriorates thecrystallinity of a crystal grown on the gap.

With the sub step above, a plurality of GaN mother crystal pieces 1 pare obtained that are arranged adjacently to each other in the lateraldirection so that respective main surfaces 1 pm of a plurality of GaNmother crystal pieces ip are parallel to each other and respective[0001] directions of the mother crystal pieces are identical, and mainsurface 1 pm has the plane orientation inclined by not less than 65° andnot more than 85° with respect to plane 1 c that is one of a (0001)plane and a (000-1) plane.

Then, referring to FIG. 5 (C), in the step of growing GaN seed crystal10 on main surfaces 1 pm of a plurality of GaN mother crystal pieces 1p, the method of growing GaN seed crystal 10 is not limited to aparticular one. In order to epitaxially grow the GaN seed crystal,preferably any of vapor phase methods such as HVPE and MOCVD and liquidphase methods such as flux method is used. Among the crystal growthmethods, the HVPE method is preferable because it provides a highcrystal growth rate.

When GaN seed crystal 10 has been grown on main surfaces 1 pm of aplurality of GaN mother crystal pieces 1 p, a crystal growth surface 10g of GaN seed crystal 10 is macroscopically parallel with main surfaces1 pm of a plurality of GaN mother crystal pieces 1 p. Microscopically,however, a plurality of facets 10 fa, 10 fb that are not in parallelwith main surfaces 1 pm of a plurality of GaN mother crystal pieces 1 pare formed. Such a plurality of facets 10 fa, 10 fb have respectiveplane orientations different from each other. Namely, GaN seed crystal10 is grown with crystal growth surface 10 g including a plurality offacets 10 fa, 10 fb having respective plane orientations different fromeach other.

Here, because facet 10 fa and facet 10 fb of crystal growth surface 10 ghave respective plane orientations different from each other, respectivecrystal-element sequences in facet 10 fa and in facet 10 fb aredifferent from each other. Therefore, in a growth portion where facet 10fa is the crystal growth surface and in a growth portion where facet 10fb is the crystal growth surface, respective directions of dislocationpropagation are different from each other.

Therefore, in GaN seed crystal 10 grown on main surfaces 1 pm of aplurality of GaN mother crystal pieces 1 p, a variation of thedislocation density is generated in a plane that is parallel with mainsurfaces 1 pm of the mother crystal pieces, resulting in a microscopicvariation of distortion in a plane that is parallel with main surfaces 1pm of the mother crystal pieces.

At this time, if the inclination of the plane orientation of mainsurfaces 1 pm of a plurality of GaN mother crystal pieces 1 p withrespect to plane 1 c that is one of a (0001) plane and a (000-1) planeis small, for example, if angle α of the inclination is smaller than65°, crystal growth surface 10 g of GaN seed crystal 10 grown on mainsurfaces 1 pm is accordingly accompanied by facet 10 fa having the planeorientation (0001) or (000-1) and facet 10 fb having a plane orientationdifferent from facet 10 fa. Here, in a growth portion where facet 10 fahaving the plane orientation (0001) or (000-1) is the crystal growthsurface, dislocation propagates in the direction perpendicular to (0001)or (000-1) (namely the <0001> direction). In a growth portion wherefacet 10 fb having a plane orientation other than (0001) and (000-1) isthe crystal growth surface, dislocation propagates in a directioninclined relative to the <0001> direction. Thus, in GaN seed crystal 10grown on main surfaces 1 pm and in main surface 10 pm of GaN seedcrystal substrate 100 p obtained from the seed crystal, a largevariation of the dislocation density is generated. Further, because of amicroscopic variation of distortion in GaN seed crystal 10 and in mainsurface 10 pm of GaN seed crystal substrate 10 p obtained from the seedcrystal, a large distortion is locally generated in a portion grown onsuch main surfaces 1 pm. Accordingly, a semiconductor device using sucha substrate has a large variation of device characteristics.

In contrast, if the inclination of the plane orientation of mainsurfaces 1 pm of a plurality of GaN mother crystal pieces 1 p withrespect to plane 1 c that is one of a (0001) plane and a (000-1) planeis large and close to the right angle, for example, if angle α of theinclination is larger than 85°, facets 10 fb having the planeorientation perpendicular to (0001) are predominantly generated atcrystal growth surface 10 g of GaN seed crystal 10 grown on mainsurfaces 1 pm. Therefore, GaN seed crystal 10 as grown is partiallypolycrystallized, resulting in a crack in GaN seed crystal 10.

In view of the above, in order to manufacture GaN seed crystal substrate10 p, it is required that the plane orientation of main surfaces 1 pm ofa plurality of GaN mother crystal pieces 1 p has inclination angle α ofnot less than 65° and not more than 85° with respect to plane 1 c thatis one of a (0001) plane and a (000-1) plane, the inclination angle ispreferably not less than 70° and not more than 80° and more preferablynot less than 72° and not more than 78°.

Referring next to FIGS. 5 (C) and (D), in the step of forming GaN seedcrystal substrate 10 p by cutting GaN seed crystal 10 along planes 10 u,10 v that are parallel with main surfaces 1 pm of a plurality of GaNmother crystal pieces 1 p, the method of cutting out GaN seed crystalsubstrate 10 p from GaN seed crystal 10 is not limited to a particularone, and may use any of various means such as wire saw, inner peripheralblade, outer peripheral blade, or laser, for example.

In order to grow a GaN single crystal of high crystallinity, averageroughness Ra of main surface 10 pm of GaN seed crystal substrate 10 p ispreferably not more than 50 nm and more preferably not more than 5 nm.The definition and the way to measure average roughness Ra of thesurface are similar to the above-described ones. In order that averageroughness Ra of main surface 10 pm of GaN seed crystal substrate 10 pmay be preferably not more than 50 nm and more preferably not more than5 nm, it is preferable that cut-out GaN seed crystal substrate 10 p hasmain surface 10 pm and side surface that are ground and/or polished.Polishing includes mechanical polishing, CMP (chemical mechanicalpolishing) and the like.

Through the above-described sub steps, referring to FIG. 5 (D) and FIG.6 (A), GaN seed crystal substrate 10 p is prepared that has main surface10 pm with an area of not less than 10 cm² and with the planeorientation inclined by not less than 65° and not more than 85° withrespect to plane 10 c that is one of a (0001) plane and a (000-1) plane.

In the case where a GaN mother crystal with a considerably largethickness is obtained, the above-described sub steps may be replacedwith the following process. Namely, such a GaN mother crystal is cutalong a plane that is parallel with the plane orientation {hkil}inclined by inclination angle α of not less than 65° and not more than85° with respect to one of a (0001) plane and a (000-1) plane of the GaNmother crystal (along a plane perpendicular to the <hkil> direction),and the main surface is ground and/or polished, so that GaN seed crystalsubstrate 10 p with main surface 10 pm having an area of not less than10 cm² and with the plane orientation inclined by not less than 65° andnot more than 85° with respect to one of a (0001) plane and a (000-1)plane is prepared.

Step of Growing GaN Single Crystal:

Then, referring to FIG. 6 (B), in the step of growing GaN single crystal20 on main surface 10 pm of GaN seed crystal substrate 10 p, the methodof growing GaN single crystal 20 is not limited to a particular one. Inorder to epitaxially grow the GaN single crystal, preferably any ofvapor phase methods such as HVPE and MOCVD and liquid phase methods suchas flux method is used. Among the crystal growth methods, the HVPEmethod is preferable because it provides a high crystal growth rate.

When GaN single crystal 20 has been grown on main surface 10 pm of GaNseed crystal substrate 10 p, crystal growth surface 20 g of GaN singlecrystal 20 is macroscopically parallel with main surface 10 pm of GaNseed crystal substrate 10 p. Microscopically, however, a plurality offacets 20 fa, 20 fb that are not in parallel with main surface 10 pm ofGaN seed crystal substrate 10 p are formed. Such a plurality of facets20 fa, 20 fb have respective plane orientations different from eachother. Namely, GaN single crystal 20 is grown with crystal growthsurface 20 g including facet surfaces 20 fa, 20 fb having respectiveplane orientations different from each other.

Here, because facet 20 fa and facet 20 fb of crystal growth surface 20 ghave respective plane orientations different from each other, respectivecrystal-element sequences in facet 20 fa and in facet 20 fb are alsodifferent from each other. Therefore, in a growth portion where facet 20fa is the crystal growth surface and in a growth portion where facet 20fb is the crystal growth surface, respective directions of dislocationpropagation are different from each other.

Therefore, in GaN single crystal 20 grown on main surface 10 pm of GaNseed crystal substrate 10 p, a variation of the dislocation density isgenerated in a plane that is parallel with main surface 10 pm of GaNseed crystal substrate 100 p. Further, in GaN single crystal 20 grown onmain surface 10 pm of GaN seed crystal substrate 10 p, a microscopicvariation of distortion is generated in a plane that is parallel withmain surface 10 pm of GaN seed crystal substrate 10 p.

At this time, if the inclination of the plane orientation of mainsurface 10 pm of GaN seed crystal substrate 10 p with respect to plane10 c that is one of a (0001) plane and a (000-1) plane is small, forexample, if angle α of the inclination is smaller than 65°, crystalgrowth surface 20 g of GaN single crystal 20 grown on main surface 10 pmis accordingly accompanied by facet 20 fa having the plane orientation(0001) or (000-1) and facet 20 fb having a plane orientation differentfrom facet 20 fa. Here, in a growth portion where facet 20 fa having theplane orientation (0001) or (000-1) is the crystal growth surface,dislocation propagates in the direction perpendicular to (0001) or(000-1) (namely the <0001> direction). In a growth portion where facet20 fb having a plane orientation other than (0001) and (000-1) is thecrystal growth surface, dislocation propagates in a direction inclinedrelative to the <0001> direction.

Thus, in GaN single crystal 20 grown on main surface 10 pm and in mainsurface 20 pm of GaN single crystal substrate 20 p obtained from thesingle crystal, a large variation of the dislocation density isgenerated. Further, because of a microscopic variation of distortion inGaN single crystal 20 grown on main surface 10 pm and in main surface 20pm of GaN single crystal substrate 20 p obtained from the singlecrystal, a large distortion is locally generated. Accordingly, asemiconductor device using such a substrate has a large variation ofdevice characteristics.

In contrast, if the inclination of the plane orientation of main surface10 pm of GaN seed crystal substrate 10 p with respect to plane 100 cthat is one of a (0001) plane and a (000-1) plane is large and close tothe right angle, for example, if angle α of the inclination is largerthan 85°, facets 20 fb having the plane orientation perpendicular to(0001) are predominantly generated at crystal growth surface 20 g of GaNsingle crystal 20 grown on main surface 10 pm. Therefore, GaN singlecrystal 20 as grown is partially polycrystallized, resulting in a crackin GaN single crystal 20.

In view of the above, in order to manufacture GaN single crystalsubstrate 20 p having a substantially uniform distribution of thedislocation density in main surface 20 pm, and in order to manufactureGaN single crystal substrate 20 p having a photoelastisity distortionvalue of not more than 5×10⁻⁵ in main surface 20 pm, it is required thatthe plane orientation of main surface 10 pm of GaN seed crystalsubstrate 10 p has inclination angle α of not less than 65° and not morethan 85° with respect to plane 10 c that is one of a (0001) plane and a(000-1) plane, the inclination angle is preferably not less than 70° andnot more than 80° and more preferably not less than 72° and not morethan 78°.

Step of Forming GaN Single Crystal Substrate:

Referring next to FIGS. 6 (B) and (C), in the step of forming GaN singlecrystal substrate 20 p by cutting out GaN single crystal substrate 20 pfrom GaN single crystal 20 along planes 20 u, 20 v that are parallelwith main surface 10 pm of GaN seed crystal substrate 10 p, the methodof cutting out GaN single crystal substrate 20 p from GaN single crystal20 is not limited to a particular one, and may use any of various meanssuch as wire saw, inner peripheral blade, outer peripheral blade, orlaser, for example.

In order to grow a GaN-based semiconductor layer of high crystallinity,average roughness Ra of main surface 20 pm of GaN single crystalsubstrate 20 p is preferably not more than 50 nm and more preferably notmore than 5 nm. The definition and the way to measure average roughnessRa of the surface are similar to the above-described ones. In order thataverage roughness Ra of main surface 20 pm of GaN single crystalsubstrate 20 p may be preferably not more than 50 nm and more preferablynot more than 5 nm, it is preferable that cut-out GaN single crystalsubstrate 20 p has main surface 20 pm and side surface that are groundand/or polished. Polishing includes mechanical polishing. CMP (chemicalmechanical polishing) and the like.

Through the above-described steps, GaN single crystal substrate 20 p isobtained that has main surface 20 pm with an area of not less than 10cm² and with the plane orientation inclined by not less than 65° and notmore than 850 with respect to plane 20 c that is one of a (0001) planeand a (000-1) plane, has a substantially uniform distribution of thedislocation density in main surface 20 pm (for example, a variation ofthe dislocation density in main surface 20 pm is within ±100% withrespect to an average dislocation density in this main surface 20 pm),and has a photoelasticity distortion value of not more than 5×10⁻⁵measured by photoelasticity at an arbitrary point in main surface 20 pmwhen light is applied perpendicularly to main surface 20 pm at anambient temperature of 25° C.

GaN-Based Semiconductor Device Embodiment 3

Referring to FIG. 8, a GaN-based semiconductor device 100 in a furtherembodiment of the present invention includes GaN single crystalsubstrate 20 p in Embodiment 1, and at least one GaN-based semiconductorlayer 130 formed on main surface 20 pm of GaN single crystal substrate20 p.

In GaN-based semiconductor device 100 in the present embodiment, GaNsingle crystal substrate 20 p has main surface 20 pm with an area of notless than 10 cm², the plane orientation of main surface 20 pm isinclined by not less than 65° and not more than 85° with respect toplane 20 c that is one of a (0001) plane and a (000-1) plane, and GaNsingle crystal substrate 20 p has at least one of a substantiallyuniform distribution of the carrier concentration in main surface 20 pm(for example, a variation of the carrier concentration in main surface20 pm is within ±50% with respect to an average carrier concentration inthis main surface 20 pm), a substantially uniform distribution of thedislocation density in main surface 20 pm (for example, a variation ofthe dislocation density in main surface 20 pm is within ±100% withrespect to an average dislocation density in this main surface 20 pm),and a photoelasticity distortion value of not more than 5×10⁻⁵ where thephotoelasticity distortion value is measured by photoelasticity at anarbitrary point in main surface 20 pm when light is appliedperpendicularly to main surface 20 pm at an ambient temperature of 25°C. Thus, the GaN-based semiconductor device in the present embodimenthas a substantially uniform distribution of device characteristics inthe main surface and has superior device characteristics. Regarding thedevice in the present embodiment, in the case for example where anelectrode is formed on GaN single crystal substrate 20 p in which thedistribution of the carrier concentration in main surface 20 pm issubstantially uniform, the distribution of the contact resistancebetween the single crystal substrate and the electrode is substantiallyuniform.

Referring to FIG. 8, GaN-based semiconductor device 100 in the presentembodiment includes, on one main surface 20 pm of GaN single crystalsubstrate 20 p of 50 mm in diameter×500 μm in thickness, at least oneGaN-based semiconductor layer 130 is formed. This GaN-basedsemiconductor layer includes an Si-doped n-type GaN layer 131 having athickness of 2 μm, a light emitting layer 132 having a multiple quantumwell structure formed of six pairs of an In_(0.01)Ga_(0.99)N barrierlayer and an In_(0.1)Ga_(0.9)N well layer and having a thickness of 100nm, an Mg-doped p-type Al_(0.18)Ga_(0.82)N layer 133 having a thicknessof 20 nm, and an Mg-doped p-type GaN layer 134 having a thickness of 50nm that are stacked in order. On a part of the surface of p-type GaNlayer 134, an Ni/Au electrode of 0.2 mm×0.2 mm×0.5 μm in thickness thatis a p-side electrode 141 is formed. Further, on another main surface 20pn of GaN single crystal substrate 20 p, a Ti/Al electrode that is ann-side electrode 142 with a thickness of 1 μm is formed

Method of Manufacturing GaN-Based Semiconductor Device Embodiment 4

Referring to FIG. 8, a method of manufacturing GaN-based semiconductordevice 100 in a further embodiment of the present invention includes thestep of preparing GaN single crystal substrate 20 p in Embodiment 1, andthe step of growing at least one GaN-based semiconductor layer 130 onmain surface 20 pm of GaN single crystal substrate 20 p.

According to the method of manufacturing GaN-based semiconductor device100 in the present embodiment, at least one GaN-based semiconductorlayer 130 is epitaxially grown on GaN single crystal substrate 20 p.Main surface 20 pm of GaN single crystal substrate 20 p has an area ofnot less than 10 cm². The plane orientation of main surface 20 pm isinclined by not less than 65° and not more than 85° with respect toplane 20 c that is one of a (0001) plane and a (000-1) plane. GaN singlecrystal substrate 20 p has at least one of a substantially uniformdistribution of the carrier concentration in main surface 20 pm (forexample, a variation of the carrier concentration in main surface 20 pmis within ±50% with respect to an average carrier concentration in thismain surface 20 pm), a substantially uniform distribution of thedislocation density in main surface 20 pm (for example, a variation ofthe dislocation density in main surface 20 pm is within ±100% withrespect to an average dislocation density in this main surface 20 pm),and a photoelasticity distortion value of not more than 5×10⁻⁵ where thephotoelasticity distortion value is measured by photoelasticity at anarbitrary point in main surface 20 pm when light is appliedperpendicularly to main surface 20 pm at an ambient temperature of 25°C. Thus, the method of manufacturing a GaN-based semiconductor device inthe present embodiment provides the GaN-based semiconductor devicehaving a substantially uniform distribution of device characteristics inthe main surface and having superior device characteristics. Forexample, when an electrode is formed on GaN single crystal substrate 20p having at least one of a substantially uniform distribution of thecarrier concentration in main surface 20 pm, a substantially uniformdistribution of the dislocation density in main surface 20 pm, and aphotoelasticity distortion value of not more than 5×10⁻⁵ where thephotoelasticity distortion value is measured by photoelasticity at anarbitrary point in main surface 20 pm when light is appliedperpendicularly to main surface 20 pm at an ambient temperature of 25°C., the distribution of the contact resistance between the singlecrystal substrate and the electrode is substantially uniform.

The step of preparing GaN single crystal substrate 20 p in Embodiment 1is performed following the method of manufacturing GaN single crystalsubstrate 20 p in Embodiment 2 above, for example. Here, GaN singlecrystal substrate 20 p in Embodiment 1 has main surface 20 pm with anarea of not less than 10 cm² and with the plane orientation inclined bynot less than 65° and not more than 85° with respect to plane 20 c thatis one of a (0001) plane and a (000-1) plane, and has at least one of asubstantially uniform distribution of the carrier concentration in mainsurface 20 pm (for example, a variation of the carrier concentration inmain surface 20 pm is within ±50% with respect to an average carrierconcentration in this main surface 20 pm), a substantially uniformdistribution of the dislocation density in main surface 20 pm (forexample, a variation of the dislocation density in main surface 20 pm iswithin ±100% with respect to an average dislocation density in this mainsurface 20 pm), and a photoelasticity distortion value of not more than5×10⁻⁵ where the photoelasticity distortion value is measured byphotoelasticity at an arbitrary point in main surface 20 pm when lightis applied perpendicularly to main surface 20 pm at an ambienttemperature of 25° C.

The method of growing at least one GaN-based semiconductor layer 130 onmain surface 20 pm of GaN single crystal substrate 20 p is not limitedto a particular one. For the sake of epitaxial growth of GaN-basedsemiconductor layer 130 of high crystallinity, HVPE, MOCVD, MBE(Molecular Beam Epitaxy) or the like is preferably used. For the sake ofhigh productivity and high reliability. MOCVD is more preferably used.

Referring to FIG. 8, in the step of forming at least one GaN-basedsemiconductor layer 130 on GaN single crystal substrate 20 p, MOCVD isused to grow at least one GaN-based semiconductor layer 130 on one mainsurface 20 pm of GaN single crystal substrate 20 p of 50 mm indiameter×0.4 mm in thickness, for example. Specifically, Si-doped n-typeGaN layer 131 having a thickness of 2 μm, light emitting layer 132having a multiple quantum well structure formed of six pairs of anIn_(0.01)Ga_(0.99)N barrier layer and an In_(0.18)Ga_(0.9)N well layerand having a thickness of 100 nm, Mg-doped p-type Al_(0.18)Ga_(0.82)Nlayer 133 having a thickness of 20 nm, and Mg-doped p-type GaN layer 134having a thickness of 50 nm are grown in order.

Further, on a part of the surface of p-type GaN layer 134, the Ni/Auelectrode of 0.5 μm in thickness is formed as p-side electrode 141 bymeans of the vacuum deposition method. Further, on the other mainsurface 20 pn of GaN single crystal substrate 20 p, the Ti/Al electrodeof 1 μm in thickness is formed as n-side electrode 142 by means of thevacuum deposition method.

Next, a wafer including at least one GaN-based semiconductor layer 130formed on GaN single crystal substrate 20 p is divided into chips of apredetermined size so that a light emitting device of a predeterminedsize is obtained.

EXAMPLES Production of GaN Mother Crystal A

GaN mother crystal A was produced in the following manner. On a mainsurface of a (111) A plane of a GaAs substrate (base substrate) having adiameter of 50 mm and a thickness of 0.8 mm, an SiO layer (mask layer)was formed which had a thickness of 100 nm and in which a plurality ofopenings of 2 μm in diameter were arranged two-dimensionally in thehexagonal close-packed manner at a pitch of 4 μm, by photolithographyand etching. Next, on the main surface of the GaAs substrate on whichthe SiO layer with a plurality of openings was formed, the HVPE methodwas performed to grow a GaN low-temperature layer of 80 nm in thicknessat 500° C. Then, a GaN intermediate layer of 60 μm in thickness wasgrown at 950° C. After this, at 1050° C., GaN mother crystal A of 5 mmin thickness was grown. Next, by means of etching with aqua regia, theGaAs substrate was removed from GaN mother crystal A to obtain GaNmother crystal A having a diameter of 50 mm and a thickness of 3 mm.

Example A1

1. Preparation of GaN Seed Crystal Substrate

Referring to FIG. 3 (A), a (0001) plane and (000-1) plane 1 c that arerespectively the two main surfaces of GaN mother crystal A (GaN mothercrystal 1) were ground and polished so that average roughness Ra of thetwo main surfaces was 5 nm. Here, average roughness Ra of the surfaceswas measured by means of AFM.

Next, referring to FIG. 3 (A), GaN mother crystal 1 having averageroughness Ra of 5 nm of the two main surfaces was sliced along a planethat is parallel with the {20-21} plane (along a plane perpendicular tothe <20-21> direction), so that a plurality of GaN mother crystal pieces1 p having a main surface of (20-21) were cut out. Subsequently, thefour un-ground and un-polished sides of the cut-out GaN mother crystalpieces 1 p each were ground and polished, so that average roughness Raof these four sides was 5 nm. In this way, a plurality of GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of the mainsurface of {20-21} were obtained. These GaN mother crystal pieces 1 pincluded a crystal piece having its main surface whose plane orientationis not exactly identical to {20-21}. Regarding any of the crystalpieces, however, the plane orientation of the main surface had aninclination angle within ±0.1° with respect to {20-21}. Here, theinclination angle was measured by the x-ray diffractometry.

Next, referring to FIG. 3 (B), a plurality of GaN mother crystal pieces1 p were arranged adjacently to each other in the lateral direction, insuch a manner that respective main surfaces 1 pm of {20-21} of aplurality of GaN mother crystal pieces 1 p were parallel to each otherand respective [0001] directions of these GaN mother crystal pieces 1 pwere identical. Further, the outer peripheral portion was partiallyremoved. In this way, GaN seed crystal substrate 10 p of 50 mm indiameter was prepared.

2. Growth of GaN Single Crystal

Next, referring to FIG. 3 (C), main surface 10 pm of {20-21} of GaN seedcrystal substrate 10 p as described above was processed in a gas mixtureatmosphere of 10 vol % of hydrogen chloride gas and 90 vol % of nitrogengas and at 800° C. for two hours. After this, on this main surface 10pm, the HVPE method was performed to grow GaN single crystal 20 at acrystal growth temperature of 1050° C. and at a growth rate of 80 μm/hrfour 50 hours.

3. Formation of GaN Single Crystal Substrate

Next, referring to FIG. 3 (D), above-described GaN single crystal 20 wassliced along planes 20 u, 20 v that are parallel with main surface 10 pmof {20-21} of GaN seed crystal substrate 10 p to obtain GaN singlecrystal substrate 20 p having main surface 20 pm whose plane orientationis (20-21), and having a diameter of 50 mm and a thickness of 0.5 mm.For GaN single crystal substrate 20 p, main surface 20 pm was furtherground and polished so that average roughness Ra of main surface 20 pmwas 5 nm. Referring to FIG. 7 (A), main surface 20 pm of {20-21} of GaNsingle crystal substrate 20 p has inclination angle α of 75° withrespect to (0001) plane 20 c.

The carrier concentration in main surface 20 pm of GaN single crystalsubstrate 20 p formed in the above-described manner was measured bymeans of the van der Pauw method at 400 measurement points from thecenter toward the outer periphery in main surface 20 pm, at a pitch of 2mm along each of two directions orthogonal to each other, except formeasurement points in the peripheral portion. The average carrierconcentration was 5.7×10¹⁷ cm⁻³, the minimum carrier concentration was3.9×10¹⁷ cm⁻³, and the maximum carrier concentration was 7.2×10¹⁷ cm⁻³.Therefore, the variation of the carrier concentration relative to theaverage carrier concentration in the main surface was a small variationof −31.6% to +26.3%.

Further, the specific resistance in main surface 20 pm of GaN singlecrystal substrate 20 p was measured by means of the van der Pauw methodat 400 measurement points from the center toward the outer periphery inmain surface 20 pm, at a pitch of 2 mm along each of two directionsorthogonal to each other, except for measurement points in theperipheral portion. The average specific resistance was 0.019 Ω·cm, theminimum specific resistance was 0.014 Ω·cm, and the maximum specificresistance was 0.026 Ω·cm. Therefore, the variation of the specificresistance relative to the average specific resistance in the mainsurface was a small variation of −26% to +37%.

4. Manufacture of GaN-Based Semiconductor Device

Referring next to FIG. 8, on one main surface 20 pm of GaN singlecrystal substrate 20 p (50 mm in diameter×0.4 mm in thickness), theMOCVD method was performed to grow at least one GaN-based semiconductorlayer 130. Specifically, Si-doped n-type GaN layer 131 having athickness of 2 μm (average carrier concentration: 2×10¹⁸ cm⁻³), lightemitting layer 132 having a multiple quantum well structure formed ofsix pairs of an In_(0.01)Ga_(0.99)N barrier layer and anIn_(0.1)Ga_(0.9)N well layer and having a thickness of 100 nm, Mg-dopedp-type Al_(0.18)Ga_(0.82)N layer 133 having a thickness of 20 nm(average carrier concentration: 3×10¹⁷ cm⁻³), and Mg-doped p-type GaNlayer 134 having a thickness of 50 nm (average carrier concentration:1×10¹⁸ cm⁻³) were grown in order.

Next, by the vacuum deposition method, Ni/Au electrodes of 0.2 mm×0.2mm×0.5 μm in thickness were formed as p-side electrodes 141 at a pitchof 1 mm along two directions orthogonal to each other on p-type GaNlayer 134. Further, by the vacuum deposition method, a Ti/Al electrodeof 1 μm in thickness was formed as n-side electrode 142 on the othermain surface 20 pn of GaN single crystal substrate 20 p.

Then, a wafer including above-described at least one GaN-basedsemiconductor layer 130 formed on GaN single crystal substrate 20 p wasdivided into a plurality of chips of 1 mm×1 mm, namely GaN-basedsemiconductor devices (chips were generated from the wafer), so thateach p-side electrode is located at a center of each chip, except for anouter peripheral portion in the wafer, for which the distribution of thecarrier concentration and the specific resistance was not measured, inmain surface 20 pm of GaN single crystal substrate 20 p. GaN-basedsemiconductor device 100 obtained in this manner was an LED (lightemitting diode) having an emission peak wavelength of 450 nm.

The brightness of the main surface of the LED (GaN-based semiconductordevice 100) manufactured in the above-described manner was measured bymeans of a brightness measurement integrating sphere, for 1600 LEDs inthe form of chips as described above. The average brightness of LEDsobtained in the present Example A1 was used as an average relativebrightness of 1.0, and the average relative brightness as well as thesample variance of the relative brightness were expressed for each ofExamples A1 to A4 and Comparative Examples RA3, RA4. The LEDsmanufactured in this Example A1 had a large average relative brightnessof 1.0, and a small sample variance of the relative brightness of 0.12.The results are summarized in Table 1.

Example A2

Referring to FIG. 3 (A) to (D), GaN single crystal substrate 20 p havingmain surface 20 pm with the plane orientation of {20-2-1} was formedsimilarly to Example A1 except that, in the step of preparing GaN seedcrystal substrate 10 p, GaN mother crystal A (GaN mother crystal 1)having average roughness Ra of 5 nm of the two main surfaces was slicedalong a plane that is parallel with the {20-2-1} plane (along a planeperpendicular to the <20-2-1> direction) so as to cut out a plurality ofGaN mother crystal pieces 1 p each having a main surface of {20-2-1},the main surfaces of the crystal pieces were ground and polished, andresultant GaN mother crystal pieces 1 p having average roughness Ra of 5nm of respective main surfaces were used. Referring to FIG. 7 (B), mainsurface 20 pm of {20-2-1} of GaN single crystal substrate 20 p hasinclination angle α of 75° relative to (000-1) plane 20 c.

As to the carrier concentration in main surface 20 pm of GaN singlecrystal substrate 20 p formed in the above-described manner, the averagecarrier concentration was 7.1×10¹⁷ cm⁻³, the minimum carrierconcentration was 5.0×10¹⁷ cm⁻³, and the maximum carrier concentrationwas 8.2×10¹⁷ cm⁻³. Therefore, the variation of the carrier concentrationrelative to the average carrier concentration in the main surface was asmall variation of −29.6% to +15.5%. As to the specific resistance inmain surface 20 pm of GaN single crystal substrate 20 p, the averagespecific resistance was 0.016 Ω·cm, the minimum specific resistance was0.012 Ω·cm, and the maximum specific resistance was 0.020 Ω·cm.Therefore, the variation of the specific resistance relative to theaverage specific resistance in the main surface was a small variation of−25% to +25%.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample A1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 1.2 and a small sample variance ofthe relative brightness of 0.11. The results are summarized in Table 1.

Example A3

Referring to FIG. 3 (A) to (D). GaN single crystal substrate 20 p havingmain surface 20 pm with the plane orientation of {22-42} was formedsimilarly to Example A1 except that, in the step of preparing GaN seedcrystal substrate 10 p, GaN mother crystal A (GaN mother crystal 1)having average roughness Ra of 5 nm of the two main surfaces was slicedalong a plane that is parallel with the {22-42} plane (along a planeperpendicular to the <22-42> direction) so as to cut out a plurality ofGaN mother crystal pieces 1 p each having a main surface of {22-42}, themain surfaces of the crystal pieces were ground and polished, andresultant GaN mother crystal pieces 1 p having average roughness Ra of 5nm of respective main surfaces were used. Referring to FIG. 7 (C), mainsurface 20 pm of {22-42} of GaN single crystal substrate 20 p hasinclination angle α of 73° relative to (0001) plane 20 c.

As to the carrier concentration in main surface 20 pm of GaN singlecrystal substrate 20 p formed in the above-described manner, the averagecarrier concentration was 6.1×10¹⁷ cm³, the minimum carrierconcentration was 3.5×10¹⁷ cm⁻³, and the maximum carrier concentrationwas 8.7×10¹⁷ cm⁻³. Therefore, the variation of the carrier concentrationrelative to the average carrier concentration in the main surface was asmall variation of −42.6% to +42.6%. As to the specific resistance inmain surface 20 pm of GaN single crystal substrate 20 p, the averagespecific resistance was 0.020 Ω·cm, the minimum specific resistance was0.012 Ω·cm, and the maximum specific resistance was 0.029 Ω·cm.Therefore, the variation of the specific resistance relative to theaverage specific resistance in the main surface was a small variation of−40% to +45%.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample A1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 0.9 and a small sample variance ofthe relative brightness of 0.14. The results are summarized in Table 1.

Example A4

Referring to FIG. 3 (A) to (D), GaN single crystal substrate 20 p havingmain surface 20 pm with the plane orientation of {22-4-21} was formedsimilarly to Example A1 except that, in the step of preparing GaN seedcrystal substrate 10 p, GaN mother crystal A (GaN mother crystal 1)having average roughness Ra of 5 nm of the two main surfaces was slicedalong a plane that is parallel with the {22-4-2}plane (along a planeperpendicular to the <22-4-2> direction) so as to cut out a plurality ofGaN mother crystal pieces 1 p each having a main surface of {22-4-2},the main surfaces of the crystal pieces were ground and polished, andresultant GaN mother crystal pieces 1 p having average roughness Ra of 5nm of respective main surfaces were used. Referring to FIG. 7 (D), mainsurface 20 pm of {22-4-2} of GaN single crystal substrate 20 p hasinclination angle α of 73° relative to (000-1) plane 20 c.

As to the carrier concentration in main surface 20 pm of GaN singlecrystal substrate 20 p formed in the above-described manner, the averagecarrier concentration was 8.5×10¹⁷ cm⁻³, the minimum carrierconcentration was 5.0×10¹⁷ cm⁻³, and the maximum carrier concentrationwas 1.25×10¹⁷ cm⁻³. Therefore, the variation of the carrierconcentration relative to the average carrier concentration in the mainsurface was a small variation of −41.2% to +47.1%. As to the specificresistance in main surface 20 pm of GaN single crystal substrate 20 p,the average specific resistance was 0.015 Ω·cm, the minimum specificresistance was 0.008 Ω·cm, and the maximum specific resistance was 0.020Ω·cm. Therefore, the variation of the specific resistance relative tothe average specific resistance in the main surface was a smallvariation of −47% to +33%.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample A1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 0.86 and a small sample variance ofthe relative brightness of 0.14. The results are summarized in Table 1.

Comparative Example RA1

Referring to FIG. 3 (A) to (D), GaN single crystal 20 was grownsimilarly to Example A1 except that, in the step of preparing GaN seedcrystal substrate 10 p, GaN mother crystal A (GaN mother crystal 1)having average roughness Ra of 5 nm of the two main surfaces was slicedalong a plane that is parallel with the {10-10}plane (along a planeperpendicular to the <10-10> direction) so as to cut out a plurality ofGaN mother crystal pieces 1 p each having a main surface of {10-10}, themain surfaces of the crystal pieces were ground and polished, andresultant GaN mother crystal pieces 1 p having average roughness Ra of 5nm of respective main surfaces were used GaN single crystal 20 waspartially polycrystallized and cracked from the polycrystallizedportion. Therefore, a GaN single crystal substrate could not be obtainedand thus a GaN-based semiconductor device could not be manufactured. Theresults are summarized in Table 1.

Comparative Example RA2

Referring to FIG. 3 (A) to (D), GaN single crystal 20 was grownsimilarly to Example A1 except that, in the step of preparing GaN seedcrystal substrate 10 p, GaN mother crystal A (GaN mother crystal 1)having average roughness Ra of 5 nm of the two main surfaces was slicedalong a plane that is parallel with the (11-20; plane (along a planeperpendicular to the <11-20> direction) so as to cut out a plurality ofGaN mother crystal pieces 1 p each having a main surface of {11-20}, themain surfaces of the crystal pieces were ground and polished, andresultant GaN mother crystal pieces 1 p having average roughness Ra of 5nm of respective main surfaces were used GaN single crystal 20 waspartially polycrystallized and cracked from the polycrystallizedportion. Therefore, a GaN single crystal substrate could not be obtainedand thus a GaN-based semiconductor device could not be manufactured. Theresults are summarized in Table 1.

Comparative Example RA3

Referring to FIG. 3 (A) to (D), GaN single crystal substrate 20 p havingmain surface 20 pm with the plane orientation of {10-11} was formedsimilarly to Example A1 except that, in the step of preparing GaN seedcrystal substrate 10 p, GaN mother crystal A (GaN mother crystal 1)having average roughness Ra of 5 nm of the two main surfaces was slicedalong a plane that is parallel with the {10-11} plane (along a planeperpendicular to the <10-11> direction) so as to cut out a plurality ofGaN mother crystal pieces 1 p each having a main surface of {10-11}, themain surfaces of the crystal pieces were ground and polished, andresultant GaN mother crystal pieces 1 p having average roughness Ra of 5nm of respective main surfaces were used. The main surface of {10-11} ofGaN single crystal substrate 20 p has inclination angle α of 62°relative to a (0001) plane.

As to the carrier concentration in main surface 20 pm of GaN singlecrystal substrate 20 p formed in the above-described manner, the averagecarrier concentration was 4.5×10¹⁷ cm⁻³, the minimum carrierconcentration was 3.5×10¹⁷ cm⁻³, and the maximum carrier concentrationwas 7.1×10¹⁷ cm⁻³. Therefore, the variation of the carrier concentrationrelative to the average carrier concentration in the main surface was alarge variation of −92.2% to +57.8%. As to the specific resistance inmain surface 20 pm of GaN single crystal substrate 20 p, the averagespecific resistance was 0.073 Ω·cm, the minimum specific resistance was0.014 Ω·cm, and the maximum specific resistance was 0.29 Ω·cm.Therefore, the variation of the specific resistance relative to theaverage specific resistance in the main surface was a large variation of−81% to +297%.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample A1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had asmall average relative brightness of 0.55 and a large sample variance ofthe relative brightness of 0.35. The results are summarized in Table 1.

Comparative Example RA4

Referring to FIG. 3 (A) to (D), GaN single crystal substrate 20 p havingmain surface 20 pm with the plane orientation of {11-22} was formedsimilarly to Example A1 except that, in the step of preparing GaN seedcrystal substrate 10 p, GaN mother crystal A (GaN mother crystal 1)having average roughness Ra of 5 nm of the two main surfaces was slicedalong a plane that is parallel with the {11-22} plane (along a planeperpendicular to the <11-22> direction) so as to cut out a plurality ofGaN mother crystal pieces 1 p each having a main surface of {11-22}, themain surfaces of the crystal pieces were ground and polished, andresultant GaN mother crystal pieces 1 p having average roughness Ra of 5nm of respective main surfaces were used. The main surface of {11-22} ofGaN single crystal substrate 20 p has inclination angle α of 58°relative to a (0001) plane.

As to the carrier concentration in main surface 20 pm of GaN singlecrystal substrate 20 p formed in the above-described manner, the averagecarrier concentration was 4.9×10¹⁷ cm⁻³, the minimum carrierconcentration was 3.1×10¹⁶ cm⁻³, and the maximum carrier concentrationwas 6.8×10¹⁷ cm⁻³. Therefore, the variation of the carrier concentrationrelative to the average carrier concentration in the main surface was alarge variation of −93.7% to +38.8%. As to the specific resistance inmain surface 20 pm of GaN single crystal substrate 20 p, the averagespecific resistance was 0.11 Ω·cm, the minimum specific resistance was0.015 Ω·cm, and the maximum specific resistance was 0.32 Ω·cm.Therefore, the variation of the specific resistance relative to theaverage specific resistance in the main surface was a large variation of−86% to +190%.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample A1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had asmall average relative brightness of 0.41 and a large sample variance ofthe relative brightness of 0.31. The results are summarized in Table 1.

TABLE 1 Comparative Comparative Comparative Comparative Example ExampleExample Example Example Example Example Example A1 A2 A3 A4 RA1 RA2 RA3RA4 GaN single plane orientation of main {20-21} {20-2-1} {22-42}{22-4-2} {10-10} {11-20} {10-11} {11-22} crystal surface substrateinclination angle α (°) 75 75 73 73 90 90 62 58 carrier average 5.7 7.16.1 8.5 partially partially 4.5 4.9 concentration (×10¹⁷ cm⁻³) poly-poly- min 3.9 5.0 3.5 5.0 crystallized, crystallized, 0.35 0.31 (×10¹⁷cm⁻³) cracked cracked max 7.2 8.2 8.7 12.5 7.1 6.8 (×10¹⁷ cm⁻³)variation (%) −31.6 to −29.6 to −42.6 to −41.2 to −92.2 to −93.7 to+26.3 +15.5 +42.6 +47.1 +57.8 +38.8 specific average 0.019 0.016 0.0200.015 0.073 0.11 resistance (Ω · cm) min 0.014 0.012 0.012 0.008 0.0140.015 (Ω · cm) max 0.026 0.020 0.029 0.020 0.29 0.32 (Ω · cm) variation(%) −26 to −25 to −40 to −47 to −81 to +297 −86 to +190 +37 +25 +45 +33GaN-based relative average 1.0 1.2 0.9 0.86 0.55 0.41 semi- brightnesssample 0.12 0.11 0.14 0.14 0.35 0.31 conductor variance device

As clearly seen from Table 1, a GaN single crystal substrate having amain surface of the plane orientation inclined by not less than 65° andnot more than 85° with respect to one of a (0001) plane and a (000-1)plane, and having a substantially uniform distribution of the carrierconcentration in the main surface (variation of the carrierconcentration relative to the average carrier concentration in the mainsurface is within ±50%) could be used to obtain a GaN-basedsemiconductor device having a large average emission intensity of themain surface and a substantially uniform distribution of the emissionintensity in the main surface (the sample variance of the relativebrightness with respect to the average relative brightness in the mainsurface is 0.2 or less and thus the variation of the emission intensityrelative to the average emission intensity is small)

Production of GaN Mother Crystal B

GaN mother crystal B was produced in the following manner. On a mainsurface of a (111) A plane of a GaAs substrate (base substrate) having adiameter of 50 mm and a thickness of 0.8 mm, an SiO layer (mask layer)was formed which had a thickness of 100 nm and in which a plurality ofopenings of 2 μm in diameter were arranged two-dimensionally in thehexagonal close-packed manner at a pitch of 4 μm. Next, on the mainsurface of the GaAs substrate on which the SiO layer with a plurality ofopenings was formed, the HVPE method was performed to grow a GaNlow-temperature layer of 80 nm in thickness at 500° C. Then, a GaNintermediate layer of 60 μm in thickness was grown at 950° C. Afterthis, at 1050° C., GaN mother crystal B of 5 mm in thickness was grown.Next, by means of etching with aqua regia, the GaAs substrate wasremoved from GaN mother crystal B to obtain GaN mother crystal B havinga diameter of 50 mm and a thickness of 3 mm. The dislocation density ofa main surface of GaN mother crystal B was measured by means of the CL(cathodoluminescence) method. Specifically, the dislocation density wasmeasured at a pitch of 2 mm along two directions orthogonal to eachother for a measurement area of 100 μm×100 μm in main surface 20 pm. Theaverage dislocation density was 3.1×10⁶ cm⁻², the minimum dislocationdensity was 0.7×10⁶ cm⁻², and the maximum dislocation density was5.5×10⁶ cm⁻².

Example B1

1. Preparation of GaN Seed Crystal Substrate

Referring to FIG. 5 (A), (0001) and (000-1) planes that are respectivelythe two main surfaces of GaN mother crystal B (GaN mother crystal 1)were ground and polished so that average roughness Ra of the two mainsurfaces was 5 nm. Here, average roughness Ra of the surfaces wasmeasured by means of AFM.

Next, referring to FIG. 5 (A), GaN mother crystal 1 having averageroughness Ra of 5 nm of the two main surfaces was sliced along a planethat is parallel with the {20-21}plane (along a plane perpendicular tothe <20-21> direction), so that a plurality of GaN mother crystal pieces1 p having a main surface of {20-21} were cut out.

Subsequently, the four un-ground and un-polished sides of the cut-outGaN mother crystal pieces 1 each were ground and polished, so thataverage roughness Ra of these four sides was 5 nm. In this way, aplurality of GaN mother crystal pieces 1 p having average roughness Raof 5 nm of the main surface of {20-21} were obtained. These GaN mothercrystal pieces 1 p included a crystal piece having its main surfacewhose plane orientation is not exactly identical to {20-21}. Regardingany of the crystal pieces, however, the plane orientation of the mainsurface had an inclination angle within ±0.1° with respect to {20-21}.Here, the inclination angle was measured by the x-ray diffractometry.

Next, referring to FIG. 5 (B), a plurality of GaN mother crystal pieces1 p were arranged adjacently to each other in the lateral direction, insuch a manner that respective main surfaces 1 pm of {20-21} of aplurality of GaN mother crystal pieces 1 p were parallel to each otherand respective [0001] directions of these GaN mother crystal pieces 1 pwere identical. Further, the outer peripheral portion was partiallyremoved so that the diameter was 50 mm.

Next, referring to FIG. 5 (C), main surfaces 1 pm of {20-21} of aplurality of GaN mother crystal pieces 1 p as described above wereprocessed in a gas mixture atmosphere of 10 vol % of hydrogen chloridegas and 90 vol % of nitrogen gas and at 800° C. for two hours. Afterthis, on main surfaces 1 pm, the HVPE method was performed to grow GaNseed crystal 10 at a crystal growth temperature of 1050° C. and at agrowth rate of 80 μm/hr four 50 hours.

Next, referring to FIGS. 5 (C), (D) and FIG. 6 (A), above-described GaNseed crystal 10 was sliced along planes 10 u, 10 v that are parallelwith main surfaces 1 pm of {20-21} of a plurality of GaN mother crystalpieces 1 p to obtain GaN seed crystal substrate 10 p having main surface10 pm with the plane orientation of {20-21}, and having a diameter of 50mm and a thickness of 0.5 mm. For GaN seed crystal substrate 10 p, mainsurface 10 pm was further ground and polished so that average roughnessRa of main surface 10 pm was 5 nm. Main surface 10 pm of (20-21) of GaNseed crystal substrate 10 p has inclination angle α of 75° with respectto a (0001) plane.

The dislocation density in main surface 10 pm of GaN seed crystalsubstrate 10 p formed in the above-descried manner was measured by meansof the CL (cathodoluminescence) method. Specifically, of the measurementpoints at a pitch of 2 mm along each of two directions orthogonal toeach other, 400 measurement points from the center to the outerperiphery in main surface 10 pm except for measurement points in theperipheral portion were used for measuring the dislocation density for ameasurement area of 100 μm×100 μm. The average dislocation density was1.5×10⁶ cm⁻², the minimum dislocation density was 1.0×10⁶ cm⁻², and themaximum dislocation density was 3.5×10⁶ cm⁻². Therefore, the variationof the dislocation density relative to the average dislocation densityin the main surface was a large variation of −33% to +133%. A possiblereason for this is as follows. GaN seed crystal substrate 10 p wasprepared using a plurality of GaN mother crystal pieces 1 p. Therefore,GaN seed crystal substrate 10 p had a part which was grown on a portionwhere GaN mother crystal pieces 1 p were adjacent to each other andwhich had a higher dislocation density.

2. Growth of GaN Single Crystal

Referring to FIG. 6 (B), main surface 10 pm of {20-21} of GaN seedcrystal substrate 10 p as described above was processed in a gas mixtureatmosphere of 10 vol % of hydrogen chloride gas and 90 vol % of nitrogengas and at 800° C. for two hours. After this, on this main surface 10pm, the HVPE method was performed to grow GaN single crystal 20 at acrystal growth temperature of 1050° C. and at a growth rate of 80 μm/hrfour 50 hours.

3. Formation of GaN Single Crystal Substrate

Next, referring to FIGS. 6 (B) and (C), above-described GaN singlecrystal 20 was sliced along planes 20 u, 20 v that are parallel withmain surface 10 pm of {20-21} of GaN seed crystal substrate 10 p toobtain GaN single crystal substrate 20 p having main surface 20 pm withthe plane orientation of {20-21}, and having a diameter of 50 mm and athickness of 0.5 mm. For GaN single crystal substrate 20 p, main surface20 pm was further ground and polished so that average roughness Ra ofmain surface 20 pm was 5 nm. Referring to FIG. 7 (A), main surface 20 pmof {20-21} of GaN single crystal substrate 20 p has inclination angle αof 75° with respect to a (0001) plane.

The dislocation density in main surface 20 pm of GaN single crystalsubstrate 20 p formed in the above-descried manner was measured by meansof the CL (cathodoluminescence) method. Specifically, of the measurementpoints at a pitch of 2 mm along each of two directions orthogonal toeach other, 400 measurement points from the center to the outerperiphery in main surface 20 pm except for measurement points in theperipheral portion were used for measuring the dislocation density for ameasurement area of 100 μm×100 μm. The average dislocation density was5.4×10⁵ cm⁻², the minimum dislocation density was 2.9×10⁵ cm⁻², and themaximum dislocation density was 7.5×10⁵ cm⁻². Therefore, the variationof the dislocation density relative to the average dislocation densityin the main surface was −46.3% to +38.9%.

In the whole of main surface 20 pm of GaN single crystal substrate 20 p,the half width of an x-ray diffraction peak obtained by x-raydiffraction rocking curve measurement where (0002) and (22-40) planeswere crystal planes of diffraction was a small value of 30 arcsec to 100arcsec. Thus, main surface 20 pm of GaN single crystal substrate 20 phad high crystallinity. Here, x-ray diffraction rocking curvemeasurement was performed by means of X'Pert Pro MRD of PANalytical(formerly Philips Analytical) at 400 measurement points from the centertoward the outer periphery in main surface 20 pm except for measurementpoints in the peripheral portion, at a pitch of 2 mm along each of twodirections orthogonal to each other, and with an x-ray irradiation areaof 1 mm².

4. Manufacture of GaN-Based Semiconductor Device

Referring next to FIG. 8, on one main surface 20 pm of GaN singlecrystal substrate 20 p (50 mm in diameter×0.4 mm in thickness), theMOCVD method was performed to grow at least one GaN-based semiconductorlayer 130. Specifically, Si-doped n-type GaN layer 131 having athickness of 2 μm (carrier concentration: 2×10¹⁸ cm⁻³), light emittinglayer 132 having a multiple quantum well structure formed of six pairsof an In_(0.01)Ga_(0.99)N barrier layer and an In_(0.18)Ga_(0.9)N welllayer and having a thickness of 100 nm, Mg-doped p-typeAl_(0.18)Ga_(0.82)N layer 133 having a thickness of 20 nm (carrierconcentration: 3×10¹⁷ cm⁻³), and Mg-doped p-type GaN layer 134 having athickness of 50 nm (carrier concentration: 1×10¹⁸ cm⁻³) were grown inorder.

Next, by the vacuum deposition method, Ni/Au electrodes of 0.2 mm×0.2mm×0.5 μm in thickness were formed as p-side electrodes 141 at a pitchof 1 mm along two directions orthogonal to each other on p-type GaNlayer 134. Further, by the vacuum deposition method, a Ti/Al electrodeof 1 μm in thickness was formed as n-side electrode 142 on the othermain surface 20 pn of GaN single crystal substrate 20 p.

Then, a wafer including above-described at least one GaN-basedsemiconductor layer 130 formed on GaN single crystal substrate 20 p wasdivided into a plurality of chips of 1 mm×1 mm, namely GaN-basedsemiconductor devices (chips were generated from the wafer), so thateach p-side electrode is located at a center of each chip, except for anouter peripheral portion in the wafer, for which the distribution of thecarrier concentration and the specific resistance was not measured, inmain surface 20 pm of GaN single crystal substrate 20 p. GaN-basedsemiconductor device 100 obtained in this manner was an LED (lightemitting diode) having an emission peak wavelength of 450 nm.

The brightness of the main surface of the LED (GaN-based semiconductordevice 100) manufactured in the above-described manner was measured bymeans of a brightness measurement integrating sphere, for 1600 LEDs inthe form of chips as described above. The average brightness of LEDsobtained in the present Example B1 was used as an average relativebrightness of 1.0, and the average relative brightness as well as thesample variance of the relative brightness were expressed for each ofExamples B1 to B4 and Comparative Examples RB3, RB4. The LEDsmanufactured in this Example B1 had a large average relative brightnessof 1.0, and a small sample variance of the relative brightness of 0.12.The results are summarized in Table 2.

Example B2

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{20-2-1} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {20-2-1} were formed similarly to ExampleB1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal B (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {20-2-1} plane (along a plane perpendicular to the<20-2-1> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {20-2-1}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of respectivemain surfaces were used. Referring to FIG. 7 (B), main surface 20 pm of{20-2-1} of GaN single crystal substrate 20 p has inclination angle α of75° relative to a (000-1) plane.

As to the dislocation density in main surface 10 pm of resultant GaNseed crystal substrate 10 p, the average dislocation density was 1.1×10⁶cm⁻², the minimum dislocation density was 7.8×10⁵ cm⁻², and the maximumdislocation density was 2.4×10⁶ cm⁻². Therefore, the variation of thedislocation density relative to the average dislocation density in themain surface was a large variation of −29% to +118%.

In contrast, as to the dislocation density in main surface 20 pm ofresultant GaN single crystal substrate 20 p, the average dislocationdensity was 3.2×10⁵ cm⁻², the minimum dislocation density was 0.0×10⁵cm⁻², and the maximum dislocation density was 4.2×10⁵ cm⁻². Therefore,the variation of the dislocation density relative to the averagedislocation density in the main surface was a small variation of −100%to +31.3%. Further, in the whole of main surface 20 pm of GaN singlecrystal substrate 20 p, x-ray diffraction rocking curve measurementwhere (0002) and (22-40) planes were crystal planes of diffraction wasperformed and a half width of the x-ray diffraction peak was a smallhalf width of 30 arcsec to 100 arcsec. Thus, main surface 20 pm of GaNsingle crystal substrate 20 p had high crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample B1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 1.2 and a small sample variance ofthe relative brightness of 0.11. The results are summarized in Table 2.

Example B3

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{22-42} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {22-42} were formed similarly to ExampleB1 except that, in the step of preparing GaN seed crystal substrate 10p. GaN mother crystal B (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {22-42} plane (along a plane perpendicular to the<22-42> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {22-42}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of respectivemain surfaces were used. Referring to FIG. 7 (C), main surface 20 pm of{22-42} of GaN single crystal substrate 20 p has inclination angle α of73° relative to a (0001) plane.

As to the dislocation density in main surface 10 pm of resultant GaNseed crystal substrate 10 p, the average dislocation density was 1.6×10⁶cm⁻², the minimum dislocation density was 1.2×10⁶ cm⁻², and the maximumdislocation density was 3.9×10⁶ cm⁻². Therefore, the variation of thedislocation density relative to the average dislocation density in themain surface was a large variation of −25% to +144%.

In contrast, as to the dislocation density in main surface 20 pm ofresultant GaN single crystal substrate 20 p, the average dislocationdensity was 6.9×10⁵ cm⁻², the minimum dislocation density was 3.5×10⁵cm⁻², and the maximum dislocation density was 9.8×10⁵ cm⁻². Therefore,the variation of the dislocation density relative to the averagedislocation density in the main surface was a small variation of −49.3%to +42.0%. Further, in the whole of main surface 20 pm of GaN singlecrystal substrate 20 p, x-ray diffraction rocking curve measurementwhere (0002) and (20-20) planes were crystal planes of diffraction wasperformed and a half width of the x-ray diffraction peak was a smallhalf width of 30 arcsec to 100 arcsec. Thus, main surface 20 pm of GaNsingle crystal substrate 20 p had high crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample B1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 0.9 and a small sample variance ofthe relative brightness of 0.14. The results are summarized in Table 2

Example B4

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{22-4-2} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {22-4-2} were formed similarly to ExampleB1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal B (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {22-4-2} plane (along a plane perpendicular to the<22-4-2> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {22-4-2}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces ip having average roughness Ra of 5 nm of respective mainsurfaces were used. Referring to FIG. 7 (D), main surface 20 pm of{22-4-2} of GaN single crystal substrate 20 p has inclination angle α of73° relative to a (000-1) plane.

As to the dislocation density in main surface 10 pm of resultant GaNseed crystal substrate 10 p, the average dislocation density was 2.2×10⁶cm⁻², the minimum dislocation density was 1.4×10⁶ cm⁻², and the maximumdislocation density was 5.5×10⁶ cm⁻². Therefore, the variation of thedislocation density relative to the average dislocation density in themain surface was a large variation of −36% to +150%.

In contrast, as to the dislocation density in main surface 20 pm ofresultant GaN single crystal substrate 20 p, the average dislocationdensity was 8.9×10⁵ cm⁻², the minimum dislocation density was 3.8×10⁵cm⁻², and the maximum dislocation density was 1.5×10⁶ cm⁻². Therefore,the variation of the dislocation density relative to the averagedislocation density in the main surface was a small variation of −57.3%to +68.5%. Further, in the whole of main surface 20 pm of GaN singlecrystal substrate 20 p, x-ray diffraction rocking curve measurementwhere (0002) and (22-20) planes were crystal planes of diffraction wasperformed and a half width of the x-ray diffraction peak was a smallhalf width of 30 arcsec to 100 arcsec. Thus, main surface 20 pm of GaNsingle crystal substrate 20 p had high crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample B1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 0.86 and a small sample variance ofthe relative brightness of 0.14. The results are summarized in Table 2.

Comparative Example RB1

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystal10 was grown similarly to Example B1 except that, in the step ofpreparing GaN seed crystal substrate 10 p, GaN mother crystal B (GaNmother crystal 1) having average roughness Ra of 5 nm of the two mainsurfaces was sliced along a plane that is parallel with the {10-10}plane (along a plane perpendicular to the <10-10> direction) so as tocut out a plurality of GaN mother crystal pieces 1 p each having a mainsurface of {10-10}, the main surfaces of the crystal pieces were groundand polished, and resultant GaN mother crystal pieces 1 p having averageroughness Ra of 5 nm of respective main surfaces were used. GaN seedcrystal 10 was partially polycrystallized and cracked from thepolycrystallized portion. Therefore, a GaN seed crystal substrate couldnot be obtained and thus a GaN single crystal substrate and a GaN-basedsemiconductor device could not be manufactured. The results aresummarized in Table 2

Comparative Example RB2

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystal10 was grown similarly to Example B1 except that, in the step ofpreparing GaN seed crystal substrate 10 p, GaN mother crystal B (GaNmother crystal 1) having average roughness Ra of 5 nm of the two mainsurfaces was sliced along a plane that is parallel with the {11-20}plane (along a plane perpendicular to the <11-20> direction) so as tocut out a plurality of GaN mother crystal pieces 1 p each having a mainsurface of {11-20}, the main surfaces of the crystal pieces were groundand polished, and resultant GaN mother crystal pieces 1 p having averageroughness Ra of 5 nm of respective main surfaces were used. GaN seedcrystal 10 was partially polycrystallized and cracked from thepolycrystallized portion. Therefore, a GaN seed crystal substrate couldnot be obtained and thus a GaN single crystal substrate and a GaN-basedsemiconductor device could not be manufactured. The results aresummarized in Table 2.

Comparative Example RB3

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{10-11} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {10-11} were formed similarly to ExampleB1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal B (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {10-11} plane (along a plane perpendicular to the<10-11> direction) so as to cut out a plurality of GaN mother crystalpieces ip each having a main surface of {10-11}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of respectivemain surfaces were used. Main surface 20 pm of {10-11} of GaN singlecrystal substrate 20 p has inclination angle α of 62° relative to a(0001) plane.

As to the dislocation density in main surface 10 pm of resultant GaNseed crystal substrate 10 p, the average dislocation density was 4.0×10⁶cm⁻², the minimum dislocation density was 2.2×10⁶ cm⁻², and the maximumdislocation density was 9.5×10⁶ cm⁻². Therefore, the variation of thedislocation density relative to the average dislocation density in themain surface was a large variation of −45% to +138%.

Further, as to the dislocation density in main surface 20 pm ofresultant GaN single crystal substrate 20 p, the average dislocationdensity was 3.2×10⁶ cm⁻², the minimum dislocation density was 1.1×10⁶cm⁻², and the maximum dislocation density was 7.5×10⁶ cm⁻². Therefore,the variation of the dislocation density relative to the averagedislocation density in the main surface was a large variation of −65.7%to +134%. In the whole of main surface 20 pm of GaN single crystalsubstrate 20 p, x-ray diffraction rocking curve measurement where (0002)and (22-40) planes were crystal planes of diffraction was performed anda half width of the x-ray diffraction peak was a large half width of 120arcsec to 350 arcsec. Thus, main surface 20 pm of GaN single crystalsubstrate 20 p had low crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample B1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had asmall average relative brightness of 0.55 and a large sample variance ofthe relative brightness of 0.35. The results are summarized in Table 2.

Comparative Example RB4

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{11-22} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {11-22} were formed similarly to ExampleB1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal B (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {11-22} plane (along a plane perpendicular to the<11-22> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {11-22}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of respectivemain surfaces were used. Main surface 20 pm of {11-22} of GaN singlecrystal substrate 20 p has inclination angle α of 58° relative to a(0001) plane.

As to the dislocation density in main surface 10 pm of resultant GaNseed crystal substrate 10 p, the average dislocation density was 4.7×10⁶cm⁻², the minimum dislocation density was 2.8×10⁶ cm⁻², and the maximumdislocation density was 9.8×10⁶ cm⁻². Therefore, the variation of thedislocation density relative to the average dislocation density in themain surface was a large variation of −40% to +109%.

Further, as to the dislocation density in main surface 20 pm ofresultant GaN single crystal substrate 20 p, the average dislocationdensity was 4.6×10⁶ cm⁻², the minimum dislocation density was 2.2×10⁶cm⁻², and the maximum dislocation density was 9.3×10⁶ cm⁻². Therefore,the variation of the dislocation density relative to the averagedislocation density in the main surface was a large variation of −52.2%to +102%. In the whole of main surface 20 pm of GaN single crystalsubstrate 20 p, x-ray diffraction rocking curve measurement where (0002)and (20-20) planes were crystal planes of diffraction was performed anda half width of the x-ray diffraction peak was a large half width of 120arcsec to 350 arcsec. Thus, main surface 20 pm of GaN single crystalsubstrate 20 p had low crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample B1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had asmall average relative brightness of 0.41 and a large sample variance ofthe relative brightness of 0.31. The results are summarized in Table 2.

TABLE 2 Comparative Comparative Comparative Comparative Example ExampleExample Example Example Example Example Example B1 B2 B3 B4 RB1 RB2 RB3RB4 GaN seed plane orientation of main {20-21} {20-2-1} {22-42} {22-4-2}{10-10} {11-20} {10-11} {11-22} crystal surface substrate inclinationangle α (°) 75 75 73 73 90 90 62 58 dislocation average 15 11 16 22partially partially 40 47 density (×10⁵ cm⁻²) poly- poly- min 10 7.8 1214 crystallized, crystallized, 22 28 (×10⁵ cm⁻²) cracked cracked max 3524 39 55 95 98 (×10⁵ cm⁻²) variation (%) −33 to −29 to −25 to −36 to −45to +138 −40 to +109 +133 +118 +144 +150 GaN single plane orientation ofmain {20-21} {20-2-1} {22-42} {22-4-2} {10-11} {11-22} crystal surfacesubstrate inclination angle α (°) 75 75 73 73 62 58 dislocation average5.4 3.2 6.9 8.9 32 46 density (×10⁵ cm⁻²) mim 2.9 0.0 3.5 3.8 11 22(×10⁵ cm⁻²) max 7.5 4.2 9.8 15 75 93 (×10⁵ cm⁻²) variation (%) −46.3 to−100 to −49.3 to −57.3 to −65.7 to −52.2 to +38.9 +31.3 +42.0 +68.5 +134+102 x-ray diffraction (0002) (0002) (0002) (0002) (0002) (0002)diffraction crystal plane (22-40) (22-40) (20-20) (20-20) (22-40)(20-20) half width of 30 to 100 30 to 100 30 to 100 30 to 100 120 to 350120 to 350 peak (arcsec) GaN-based relative average 1.0 1.2 0.9 0.860.55 0.41 semiconductor brightness sample 0.12 0.11 0.14 0.14 0.35 0.31device variance

As clearly seen from Table 2, a GaN single crystal substrate having amain surface of the plane orientation inclined by not less than 65° andnot more than 85° with respect to one of a (0001) plane and a (000-1)plane, and having a substantially uniform distribution of thedislocation density in the main surface (variation of the dislocationdensity relative to the average dislocation density in the main surfaceis within ±100%) could be used to obtain a GaN-based semiconductordevice having a large average emission intensity of the main surface anda substantially uniform distribution of the emission intensity in themain surface (the sample variance of the relative brightness withrespect to the average relative brightness in the main surface is 0.2 orless and thus the variation of the emission intensity relative to theaverage emission intensity is small).

Production of GaN Mother Crystal C

GaN mother crystal C was produced in the following manner. On a mainsurface of a (111) A plane of a GaAs substrate (base substrate) having adiameter of 50 mm and a thickness of 0.8 mm, an SiO layer (mask layer)was formed which had a thickness of 100 nm and in which a plurality ofopenings of 2 μm in diameter were arranged two-dimensionally in thehexagonal close-packed manner at a pitch of 4 μm, by photolithographyand etching. Next, on the main surface of the GaAs substrate on whichthe SiO layer with a plurality of openings was formed, the HVPE methodwas performed to grow a GaN low-temperature layer of 80 nm in thicknessat 500° C. Then, a GaN intermediate layer of 60 μm in thickness wasgrown at 950° C. After this, at 1050° C., GaN mother crystal C of 5 mmin thickness was grown. Next, by means of etching with aqua regia, theGaAs substrate was removed from GaN mother crystal C to obtain GaNmother crystal C having a diameter of 50 mm and a thickness of 3 mm.Photoelasticity distortion in the main surface of GaN mother crystal Cwas measured by means of a red LD (laser diode) with a peak wavelengthof 660 nm, following the method illustrated in Embodiment 1C, at anambient temperature of 25° C. and at a pitch of 2 mm in each of twodirections orthogonal to each other in the main surface ((0001) plane 1c). Regarding the photoelasticity distortion value, the average valuewas 9.0×10⁻⁶, the minimum value was 3.1×10⁻⁷, and the maximum value was2.1×10⁻⁵.

Example C1

1. Preparation of GaN Seed Crystal Substrate

Referring to FIG. 5 (A), (0001) and (000-1) planes that are respectivelythe two main surfaces of GaN mother crystal C (GaN mother crystal 1)were ground and polished so that average roughness Ra of the two mainsurfaces was 5 nm. Here, average roughness Ra of the surfaces wasmeasured by means of AFM.

Next, referring to FIG. 5 (A), GaN mother crystal 1 having averageroughness Ra of 5 nm of the two main surfaces was sliced along a planethat is parallel with the {20-21} plane (along a plane perpendicular tothe <20-21> direction), so that a plurality of GaN mother crystal pieces1 p having a main surface of {20-21} were cut out.

Subsequently, the four un-ground and un-polished sides of the cut-outGaN mother crystal pieces 1 p each were ground and polished, so thataverage roughness Ra of these four sides was 5 nm. In this way, aplurality of GaN mother crystal pieces 1 p having average roughness Raof 5 nm of the main surface of {20-21} were obtained. These GaN mothercrystal pieces 1 p included a crystal piece having its main surfacewhose plane orientation is not exactly identical to {20-21}. Regardingany of the crystal pieces, however, the plane orientation of the mainsurface had an inclination angle within ±0.1 with respect to {20-21}.Here, the inclination angle was measured by the x-ray diffractometry.

Next, referring to FIG. 5 (B), a plurality of GaN mother crystal pieces1 p were arranged adjacently to each other in the lateral direction, insuch a manner that respective main surfaces 1 pm of {20-21} of aplurality of GaN mother crystal pieces 1 p were parallel to each otherand respective [0001] directions of these GaN mother crystal pieces 1 pwere identical. Further, the outer peripheral portion was partiallyremoved so that the diameter was 50 mm.

Next, referring to FIG. 5 (C), main surfaces 1 pm of {20-21} of aplurality of GaN mother crystal pieces 1 p as described above wereprocessed in a gas mixture atmosphere of 10 vol % of hydrogen chloridegas and 90 vol % of nitrogen gas and at 800° C. for two hours. Afterthis, on main surfaces 1 pm, the HVPE method was performed to grow GaNseed crystal 10 at a crystal growth temperature of 1050° C. and at agrowth rate of 80 μm/hr four 50 hours.

Next, referring to FIGS. 5 (C), (D) and FIG. 6 (A), above-described GaNseed crystal 10 was sliced along planes 10 u, 10 v that are parallelwith main surfaces 1 pm of {20-21} of a plurality of GaN mother crystalpieces 1 p to obtain GaN seed crystal substrate 10 p having main surface10 pm with the plane orientation of {20-21}, and having a diameter of 50mm and a thickness of 0.5 mm. For GaN seed crystal substrate 10 p, mainsurface 10 pm was further ground and polished so that average roughnessRa of main surface 10 pm was 5 nm. Main surface 10 pm of (20-21) of GaNseed crystal substrate 10 p has inclination angle α of 75° with respectto a (0001) plane.

As to the photoelasticity distortion value in main surface 10 pm of GaNseed crystal substrate 10 p formed in the above described manner, thephotoelasticity distortion was measured by means of a red LD with a peakwavelength of 660 nm, following the method illustrated in Embodiment 1C,at an ambient temperature of 25° C., and at 400 measurement points fromthe center toward the outer periphery in main surface 10 pm, except formeasurement points in the peripheral portion, among measurement pointsat a pitch of 2 mm in each of two directions orthogonal to each other.Regarding the value of the photoelasticity distortion, the average valuewas 2.1×10⁻⁵, the minimum value was 4.9×10⁻⁷, and the maximum value was7.4×10⁻⁵. Therefore, the photoelasticity distortion value in the mainsurface was a large value of 7.4×10⁻⁵ or less, and the variationrelative to the average value was also a large variation of −98% to+252%. A possible reason for this is as follows. GaN seed crystalsubstrate 10 p was prepared using a plurality of GaN mother crystalpieces 1 p. Therefore, GaN crystal substrate 10 p had a part which wasgrown on a portion where GaN mother crystal pieces 1 p were adjacent toeach other and which had a higher photoelasticity distortion value.

2. Growth of GaN Single Crystal

Referring to FIG. 6 (B), main surface 10 pm of {20-21} of GaN seedcrystal substrate 10 p as described above was processed in a gas mixtureatmosphere of 10 vol % of hydrogen chloride gas and 90 vol % of nitrogengas and at 800° C. for two hours. After this, on this main surface 10pm, the HVPE method was performed to grow GaN single crystal 20 at acrystal growth temperature of 1050° C. and at a growth rate of 80 μm/hrfour 50 hours.

3. Formation of GaN Single Crystal Substrate

Next, referring to FIGS. 6 (B) and (C), above-described GaN singlecrystal 20 was sliced along planes 20 u, 20 v that are parallel withmain surface 10 pm of {20-21} of GaN seed crystal substrate 10 p toobtain GaN single crystal substrate 20 p having main surface 20 pm withthe plane orientation of {20-21}, and having a diameter of 50 mm and athickness of 0.5 mm. For GaN single crystal substrate 20 p, main surface20 pm was further ground and polished so that average roughness Ra ofmain surface 20 pm was 5 nm. Referring to FIG. 7 (A), main surface 20 pmof {20-21} of GaN single crystal substrate 20 p has inclination angle αof 75° with respect to a (0001) plane.

As to the photoelasticity distortion value in main surface 20 pm of GaNsingle crystal substrate 20 p formed in the above described manner, thephotoelasticity distortion was measured by means of a red LD with a peakwavelength of 660 nm, following the method illustrated in Embodiment 1C,at an ambient temperature of 25° C., and at 400 measurement points fromthe center toward the outer periphery in main surface 10 pm, except formeasurement points in the peripheral portion, among measurement pointsat a pitch of 2 mm in each of two directions orthogonal to each other.Regarding the value of the photoelasticity distortion, the average valuewas 8.3×10⁻⁶, the minimum value was 2.6×10⁻⁷, and the maximum value was1.5×10⁻⁵. Therefore, the photoelasticity distortion value in the mainsurface was a small value of 1.5×10⁻⁵ or less, and the variationrelative to the average value was also a small variation of −96.9% to+80.7%.

In the whole of main surface 20 pm of GaN single crystal substrate 20 p,the half width of an x-ray diffraction peak obtained by x-raydiffraction rocking curve measurement where (0002) and (22-40) planeswere crystal planes of diffraction was a small value of 30 arcsec to 100arcsec. Thus, main surface 20 pm of GaN single crystal substrate 20 phad high crystallinity. Here, x-ray diffraction rocking curvemeasurement was performed by means of X'Pert Pro MRD of PANalytical(formerly Philips Analytical) at 400 measurement points from the centertoward the outer periphery in main surface 20 pm, except for measurementpoints in the peripheral portion, at a pitch of 2 mm along each of twodirections orthogonal to each other, and with an x-ray irradiation areaof 1 mm².

4. Manufacture of GaN-Based Semiconductor Device

Next, referring next to FIG. 8, on one main surface 20 pm of GaN singlecrystal substrate 20 p (50 mm in diameter×0.4 mm in thickness), theMOCVD method was performed to grow at least one GaN-based semiconductorlayer 130. Specifically, Si-doped n-type GaN layer 131 having athickness of 2 μm (carrier concentration: 2×10¹⁸ cm⁻³), light emittinglayer 132 having a multiple quantum well structure formed of six pairsof an In_(0.01)Ga_(0.99)N barrier layer and an In_(0.1)Ga_(0.9)N welllayer and having a thickness of 100 nm, Mg-doped p-typeA_(0.18)Ga_(0.82)N layer 133 having a thickness of 20 nm (carrierconcentration: 3×10¹⁷ cm⁻³), and Mg-doped p-type GaN layer 134 having athickness of 50 nm (carrier concentration: 1×10¹⁸ cm⁻³) were grown inorder.

Next, by the vacuum deposition method, Ni/Au electrodes of 0.2 mm×0.2mm×0.5 μm in thickness were formed as p-side electrodes 141 at a pitchof 1 mm along two directions orthogonal to each other on p-type GaNlayer 134. Further, by the vacuum deposition method, a Ti/Al electrodeof 1 μm in thickness was formed as n-side electrode 142 on the othermain surface 20 pn of GaN single crystal substrate 20 p.

Then, a wafer including above-described at least one GaN-basedsemiconductor layer 130 formed on GaN single crystal substrate 20 p wasdivided into a plurality of chips of 1 mm×1 mm, namely GaN-basedsemiconductor devices (chips were generated from the wafer), so thateach p-side electrode is located at a center of each chip, except for anouter peripheral portion in the wafer, for which the photoelasticitydistortion value was not measured, in main surface 20 pm of GaN singlecrystal substrate 20 p. GaN-based semiconductor device 100 obtained inthis manner was an LED (light emitting diode) having an emission peakwavelength of 450 nm.

The brightness of the main surface of the LED (GaN-based semiconductordevice 100) manufactured in the above-described manner was measured bymeans of a brightness measurement integrating sphere, for 1600 LEDs inthe form of chips as described above. The average brightness of LEDsobtained in the present Example C1 was used as an average relativebrightness of 1.0, and the average relative brightness as well as thesample variance of the relative brightness were expressed for each ofExamples C1 to C4 and Comparative Examples RC3, RC4. The LEDsmanufactured in this Example C1 had a large average relative brightnessof 1.0, and a small sample variance of the relative brightness of 0.15.The results are summarized in Table 3

Example C2

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 100 p having main surface 10 pm with the plane orientation of{20-2-1} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {20-2-1} were formed similarly to ExampleC1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal C (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {20-2-1} plane (along a plane perpendicular to the<20-2-1> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {20-2-1}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of respectivemain surfaces were used. Referring to FIG. 7 (B), main surface 20 pm of{20-2-1} of GaN single crystal substrate 20 p has inclination angle α of75° relative to a (000-1) plane.

As to the photoelasticity distortion value in main surface 10 pm ofresultant GaN seed crystal substrate 10 p, the average value was1.9×10⁻⁵, the minimum value was 3.2×10⁻⁷, and the maximum value was6.5×10⁻⁵. Therefore, the photoelasticity distortion value in the mainsurface was a large value of 6.5×10⁻⁵ or less, and the variationrelative to the average value was also a large variation of −98% to+242%.

In contrast, as to the photoelasticity distortion value in main surface20 pm of resultant GaN single crystal substrate 20 p, the average valuewas 5.4×10⁻⁶, the minimum value was 1.1×10⁻⁷, and the maximum value was9.4×10⁻⁶. Therefore, the photoelasticity distortion value in the mainsurface was a small value of 9.4×10⁻⁶ or less, and the variationrelative to the average was also a small variation of −98.0% to +74.1%.Further, in the whole of main surface 20 pm of GaN single crystalsubstrate 20 p, x-ray diffraction rocking curve measurement where (0002)and (22-40) planes were crystal planes of diffraction was performed anda half width of the x-ray diffraction peak was a small half width of 30arcsec to 100 arcsec. Thus, main surface 20 pm of GaN single crystalsubstrate 20 p had high crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample C1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 1.1 and a small sample variance ofthe relative brightness of 0.11. The results are summarized in Table 3.

Example C3

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{22-42} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {22-42} were formed similarly to ExampleC1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal C (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {22-42} plane (along a plane perpendicular to the<22-42> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {22-42}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of respectivemain surfaces were used. Referring to FIG. 7 (C), main surface 20 pm of{22-42} of GaN single crystal substrate 20 p has inclination angle α of73° relative to a (0001) plane.

As to the photoelasticity distortion value in main surface 10 pm ofresultant GaN seed crystal substrate 10 p, the average value was3.3×10⁻⁵, the minimum value was 1.5×10⁻⁵, and the maximum value was1.02×10⁻⁴. Therefore, the photoelasticity distortion value in the mainsurface was a large value of 1.02×10⁻⁴ or less, and the variationrelative to the average value was also a large variation of −55% to+209%.

In contrast, as to the photoelasticity distortion value in main surface20 pm of resultant GaN single crystal substrate 20 p, the average valuewas 3.2×10⁻⁵, the minimum value was 1.1×10⁻⁵, and the maximum value was4.9×10⁻⁵. Therefore, the photoelasticity distortion value in the mainsurface was a small value of 4.9×10⁻⁵ or less, and the variationrelative to the average was also a small variation of −65.6% to +53.1%.Further, in the whole of main surface 20 pm of GaN single crystalsubstrate 20 p, x-ray diffraction rocking curve measurement where (0002)and (20-20) planes were crystal planes of diffraction was performed anda half width of the x-ray diffraction peak was a small half width of 30arcsec to 100 arcsec. Thus, main surface 20 pm of GaN single crystalsubstrate 20 p had high crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample C1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 0.92 and a small sample variance ofthe relative brightness of 0.16. The results are summarized in Table 3.

Example C4

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{22-4-2} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {22-4-2} were formed similarly to ExampleC1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal C (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {22-4-2} plane (along a plane perpendicular to the<22-4-2> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {22-4-2}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of respectivemain surfaces were used. Referring to FIG. 7 (D), main surface 20 pm of{22-4-2} of GaN single crystal substrate 20 p has inclination angle atof 73° relative to a (000-1) plane.

As to the photoelasticity distortion value in main surface 10 pm ofresultant GaN seed crystal substrate 10 p, the average value was2.9×10⁻⁵, the minimum value was 1.0×10⁻⁵, and the maximum value was9.8×10⁻⁵. Therefore, the photoelasticity distortion value in the mainsurface was a large value of 9.8×10⁻⁵ or less, and the variationrelative to the average value was also a large variation of −66% to+238%.

In contrast, as to the photoelasticity distortion value in main surface20 pm of resultant GaN single crystal substrate 20 p, the average valuewas 2.1×10⁻⁵, the minimum value was 6.6×10⁻⁶, and the maximum value was3.9×10⁻⁵. Therefore, the photoelasticity distortion value in the mainsurface was a small value of 3.9×10⁻⁵ or less, and the variationrelative to the average was also a small variation of −68.6% to +85.7%.Further, in the whole of main surface 20 pm of GaN single crystalsubstrate 20 p, x-ray diffraction rocking curve measurement where (0002)and (20-20) planes were crystal planes of diffraction was performed anda half width of the x-ray diffraction peak was a small half width of 30arcsec to 100 arcsec. Thus, main surface 20 pm of GaN single crystalsubstrate 20 p had high crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample C1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had alarge average relative brightness of 0.95 and a small sample variance ofthe relative brightness of 0.13. The results are summarized in Table 3.

Comparative Example RC1

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystal10 was grown similarly to Example C1 except that, in the step ofpreparing GaN seed crystal substrate 10 p, GaN mother crystal C (GaNmother crystal 1) having average roughness Ra of 5 nm of the two mainsurfaces was sliced along a plane that is parallel with the {10-10}plane (along a plane perpendicular to the <10-10> direction) so as tocut out a plurality of GaN mother crystal pieces 1 p each having a mainsurface of {10-10}, the main surfaces of the crystal pieces were groundand polished, and resultant GaN mother crystal pieces 1 p having averageroughness Ra of 5 nm of respective main surfaces were used. GaN seedcrystal 10 was partially polycrystallized and cracked from thepolycrystallized portion. Therefore, a GaN seed crystal substrate couldnot be obtained and thus a GaN single crystal substrate and a GaN-basedsemiconductor device could not be manufactured. The results aresummarized in Table 3.

Comparative Example RC2

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystal10 was grown similarly to Example C1 except that, in the step ofpreparing GaN seed crystal substrate 10 p, GaN mother crystal C (GaNmother crystal 1) having average roughness Ra of 5 nm of the two mainsurfaces was sliced along a plane that is parallel with the {11-20}plane (along a plane perpendicular to the <11-20> direction) so as tocut out a plurality of GaN mother crystal pieces 1 p each having a mainsurface of {11-20}, the main surfaces of the crystal pieces were groundand polished, and resultant GaN mother crystal pieces 1 p having averageroughness Ra of 5 nm of respective main surfaces were used. GaN seedcrystal 10 was partially polycrystallized and cracked from thepolycrystallized portion. Therefore, a GaN seed crystal substrate couldnot be obtained and thus a GaN single crystal substrate and a GaN-basedsemiconductor device could not be manufactured. The results aresummarized in Table 3.

Comparative Example RC3

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{10-11} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {10-11} were formed similarly to ExampleC1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal C (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {10-11} plane (along a plane perpendicular to the<10-11> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {10-11}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 mm of respectivemain surfaces were used. Main surface 20 pm of {10-11} of GaN singlecrystal substrate 20 p has inclination angle α of 62° relative to a(0001) plane.

As to the photoelasticity distortion value in main surface 10 pm ofresultant GaN seed crystal substrate 10 p, the average value was1.02×10⁻⁴, the minimum value was 4.2×10⁻⁵, and the maximum value was2.6×10⁻⁴. Therefore, the photoelasticity distortion value in the mainsurface was a large value of 2.6<10⁻⁴ or less, and the variationrelative to the average was also a large variation of −59% to +155%.

Further, as to the photoelasticity distortion in main surface 20 pm ofresultant GaN single crystal substrate 20 p, the average value was9.1×10⁻⁵, the minimum value was 3 7×10⁻⁵, and the maximum value was2.5×10⁻⁴. Therefore, the photoelasticity distortion value in the mainsurface was a large value of 2.5×10⁻⁴ or less, and the variationrelative to the average was also a large variation of −59.3% to +175%.In the whole of main surface 20 pm of GaN single crystal substrate 20 p,x-ray diffraction rocking curve measurement where (0002) and (22-40)planes were crystal planes of diffraction was performed and a half widthof the x-ray diffraction peak was a large half width of 120 arcsec to350 arcsec. Thus, main surface 20 pm of GaN single crystal substrate 20p had low crystallinity.

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample C1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had asmall average relative brightness of 0.76 and a large sample variance ofthe relative brightness of 0.25. The results are summarized in Table 3.

Comparative Example RC4

Referring to FIG. 5 (A) to (D) and FIG. 6 (A) to (C), GaN seed crystalsubstrate 10 p having main surface 10 pm with the plane orientation of{11-22} and GaN single crystal substrate 20 p having main surface 20 pmwith the plane orientation of {11-22} were formed similarly to ExampleC1 except that, in the step of preparing GaN seed crystal substrate 10p, GaN mother crystal C (GaN mother crystal 1) having average roughnessRa of 5 nm of the two main surfaces was sliced along a plane that isparallel with the {11-22} plane (along a plane perpendicular to the<11-22> direction) so as to cut out a plurality of GaN mother crystalpieces 1 p each having a main surface of {11-22}, the main surfaces ofthe crystal pieces were ground and polished, and resultant GaN mothercrystal pieces 1 p having average roughness Ra of 5 nm of respectivemain surfaces were used. Main surface 20 pm of {11-22} of GaN singlecrystal substrate 20 p has inclination angle α of 58° relative to a(0001) plane.

As to the photoelasticity distortion value in main surface 10 pm ofresultant GaN seed crystal substrate 10 p, the average value was1.21×10⁻⁴, the minimum value was 5.6×10⁻⁵, and the maximum value was 33×10⁻⁴. Therefore, the photoelasticity distortion value in the mainsurface was a large value of 3.3×10⁻⁴ or less, and the variationrelative to the average was also a large variation of −54% to +173%.

Further, as to the photoelasticity distortion in main surface 20 pm ofresultant GaN single crystal substrate 20 p, the average value was1.0×10⁻⁴, the minimum value was 4.1×10⁻⁵, and the maximum value was3.1×10⁻⁴. Therefore, the photoelasticity distortion value in the mainsurface was a large value of 3.1×10⁻⁴ or less, and the variationrelative to the average was also a large variation of −59.0% to +210%.In the whole of main surface 20 pm of GaN single crystal substrate 20 p,x-ray diffraction rocking curve measurement where (0002) and (20-20)planes were crystal planes of diffraction was performed and a half widthof the x-ray diffraction peak was a large half width of 120 arcsec to350 arcsec. Thus, main surface 20 pm of GaN single crystal substrate 20p had low crystallinity

Further, this GaN single crystal substrate 20 p was used to manufactureLEDs that are each a GaN-based semiconductor device, similarly toExample C1. As to the brightness of the main surfaces of themanufactured LEDs (GaN-based semiconductor devices 100), the LEDs had asmall average relative brightness of 0.79 and a large sample variance ofthe relative brightness of 0.24. The results are summarized in Table 3.

TABLE 3 Comparative Comparative Comparative Comparative Example ExampleExample Example Example Example Example Example C1 C2 C3 C4 RC1 RC2 RC3RC4 GaN seed plane orientation of main {20-21} {20-2-1} {22-42} {22-4-2}{10-10} {11-20} {10-11} {11-22} crystal surface substrate inclinationangle α (°) 75 75 73 73 90 90 62 58 photoelasticity average 21 19 33 29partially partially 102 121 distortion (×10⁻⁶) poly- poly- value min0.49 0.32 15 10 crystallized, crystallized, 42 56 (×10⁻⁶) crackedcracked max 74 65 102 98 260 330 (×10⁻⁶) variation (%) −98 to −98 to −55to −66 to −59 to +155 −54 to +173 +252 +242 +209 +238 GaN single planeorientation of main {20-21} {20-2-1} {22-42} {22-4-2} {10-11} {11-22}crystal surface substrate inclination angle α (°) 75 75 73 73 62 58photoelasticity average 8.3 5.4 32 21 91 100 distortion (×10⁻⁶) valuemin 0.26 0.11 11 6.6 37 41 (×10⁻⁶) max 15 9.4 49 39 250 310 (×10⁻⁶)variation (%) −96.9 to −98.0 to −65.6 to −68.6 to −59.3 to −59.0 to+80.7 74.1 +53.1 +85.7 +175 +210 x-ray diffraction (0002) (0002) (0002)(0002) (0002) (0002) diffraction crystal plane (22-40) (22-40) (20-20)(20-20) (22-40) (20-20) half width of 30 to 30 to 30 to 30 to 120 to 350120 to 350 peak (arcsec) 100 100 100 100 GaN-based relative average 1.01.1 0.92 0.95 0.76 0.79 semi- brightness sample 0.15 0.11 0.16 0.13 0.250.24 conductor variance device

As clearly seen from Table 3, a GaN single crystal substrate, which hasa main surface of the plane orientation inclined by not less than 65°and not more than 85° with respect to one of a (0001) plane and a(000-1) plane, and has a photoelasticity distortion value of not morethan 5×10⁻⁵ where the photoelasticity distortion value is measured byphotoelasticity at an arbitrary point within the main surface when lightis applied perpendicularly to the main surface at an ambient temperatureof 25° C., could be used to obtain a GaN-based semiconductor devicehaving a large average emission intensity of the main surface and asubstantially uniform distribution of the emission intensity in the mainsurface (the sample variance of the relative brightness with respect tothe average relative brightness in the main surface is 0.2 or less andthus the variation of the emission intensity relative to the averageemission intensity is small).

Although the present invention has been described and illustrated indetail, it is clearly understood that the same is by way of illustrationand example only and is not to be taken by way of limitation, the scopeof the present invention being interpreted by the terms of the appendedclaims.

What is claimed is:
 1. A GaN single crystal substrate having a mainsurface with an average roughness Ra of not more than 50 nm, the mainsurface having an area of not less than 10 cm², said main surface havinga plane orientation inclined by not less than 65° and not more than 85°with respect to one of a (0001) plane and a (000-1) plane, and a halfwidth of an x-ray diffraction peak obtained by x-ray diffraction rockingcurve measurement for one of a combination of a (0002) plane and a(20-20) plane, and a combination of a (0002) plane and a (22-40) plane,not being more than 300 arcsec over on an entirety of the main surface.2. The GaN single crystal substrate according to claim 1, wherein adistribution of a dislocation density in the main surface issubstantially uniform.
 3. The GaN single crystal substrate according toclaim 1, wherein a variation of a dislocation density in the mainsurface is within ±100% with respect to an average dislocation densityin the main surface.